Here is a list of animal shelters in the state of TEXAS.  This list is in alphabetical order by city so search for organizations in your cities near you to contact.
Two places to start are here because both organizations are housing hundreds of pets that were rescued in the Houston area:
Best Friends Animal Society -- found pets, housed at Pet Reunion Pavilion at NRG Arena, 1 NRG Pkwy, Houston, TX 77054
https://bestfriends.org/hurricaneharvey/lost-and-found-pets/nrg-pets

Austin, TX,  Austin Pets Alive,  1156 W. Cesar Chavez St,  512-961-6519
https://petharbor.com/Harvey.asp?at=CAT&st=LOST
https://www.austinpetsalive.org/adopt/harvey-found-cats/
https://www.austinpetsalive.org/adopt/harvey-found-dogs/

---------------------

Alvin Animal Adoption Center - c/o Alvin Police Department
550 W SH 6, Alvin, TX 77511
Email: amiller@cityofalvin.com
Phone: 281-388-4331
Website: www.cityofalvin.com

Angleton, TX,  Brazoria County Animal Control,  3602 County Rd 45,  979-864-2265
http://brazoriacountytx.org

Angleton Animal Control Adoption Center
535 S. Anderson, Angleton, TX 77515
Phone: 979-849-9550
Website: http://www.petfinder.com/shelters/TX794.html

Aransas Pass, TX,  SPCA San Patricio County (Sandra Sue Benson Shelter),  4630 FM 1069,  361-332-1445
http://www.spcasanpatcounty.com/11_petAdoption/index.php
http://www.spcasanpatcounty.com/index.html
https://www.facebook.com/pages/Sandra-Sue-Benson-Animal-Adoption-Center-SPCA-San-Pat-County/1093670384048135

Austin, TX,  Austin Humane Society,  124 Anderson,  512-646-7347
http://www.austinhumanesociety.org

Austin, TX,  Austin Pets Alive,  1156 W. Cesar Chavez St,  512-961-6519
https://www.austinpetsalive.org/hurricane-harvey-evacuations/
https://petharbor.com/Harvey.asp?at=CAT&st=LOST
https://www.facebook.com/austinpetsalive
https://www.austinpetsalive.org/adopt/harvey-found-cats/
https://www.austinpetsalive.org/adopt/harvey-found-dogs/

Austin, TX 78702,  Austin Animal Center,  A, 7201 Levander Loop,  512-978-0500,  austinanimalcenter.org
http://www.austintexas.gov/
http://www.austintexas.gov/adoptablepets
https://www.facebook.com/AustinAnimalCenter/

Bay City, Matagorda County Shelter (Fairgrounds/Bay City)
https://www.facebook.com/pg/friendsofstray/photos/?ref=page_internal
https://www.facebook.com/groups/723178841214733/

Baytown, TX,  Baytown Humane Society,  P. O. Box 2772,  281-424-3103
http://baytownhumanesociety.org

Baytown, TX,  Baytown Animal Services,  705 N Robert C Lanier Dr,  281-422-7600
http://baytown.org/city-hall/departments/public-health/animal-services/up-for-adoption
https://www.facebook.com/pg/baytownanimalservices/photos/?tab=album&album_id=1947153058872504
https://www.facebook.com/Friends-of-Baytown-Animal-Shelter-1699343176958654/

Beaumont, TX,  Ford Park Temporary Shelter,  5115 Interstate 10 South,  409-951-5400

Beaumont, TX,  Beaumont Animal Services,  1884 Pine St,  409-838-3304 or 409-880-3794
http://beaumonttexas.gov/departments/animal-care/adopt-pet/
http://www.adoptapet.com/adoption_rescue/80241.html#featured#current_page=1#clanId=1
https://www.facebook.com/beaumontanimalservices

Beaumont, TX,  Humane Society - Southeast TX,  2050 Spidletop Ave,  409-833-0504
https://www.petfinder.com/pet-search?shelterid=TX155
https://www.facebook.com/humanesocietyofsoutheasttexas.org
https://www.facebook.com/pg/humanesocietyofsoutheasttexas.org/photos/?ref=page_internal

Bellaire, TX,  Save-a-Pet,  7005 Mapleridge,  713-622-5295

Buna, TX,  Buna Animal Hospital Drs. Foster,  34299 Highway 96 South,  409-994-5986
http://bunavet.com/
https://www.facebook.com/BunaAnimalHospital/

Carthage, TX,  Carthage Panola County Pound,  1024 US Hwy 59 N,  903-693-2877
http://www.adoptapet.com/adoption_rescue/68429.html#featured
http://savearescue.org/search-adoptable-pets/
https://www.facebook.com/furloveofanimals/

Carthage, Chris Guard
https://www.carthagetexas.us/departments/police-department/164-animal-control-division
https://www.facebook.com/chris.guard.545?fref=gs&hc_ref=ARQS_1aYkGtjqy0ulExFdbLaq-JfIlIVvR0MN9Aom_1rC0v90hKrp99fnEL6AXbOCfE&dti=515022888841691&hc_location=group

Clear Lake and League City, TX,  Second Chance Pets,  281-286-3535
http://secondchancepets.org

Cleveland Animal Control
226 Peach Street, Cleveland, TX 77327
Email: bnoey@clevelandtexas.com
Phone: 281-592-2621
Website: http://www.clevelandtexas.com/335/Pet-Adoption-Center

Conroe, TX,  Humane Society of Montgomery County,  936-441-4762

Conroe, TX,  Montgomery County Animal Control,  8535 Hwy 242,  936-442-7738
https://mcaspets.org

Conroe, TX,  Conroe Adoption Center (Montgomery County Animal Shelter),  8535 Hwy 242,  936-522-3550
https://petharbor.com/harvey.asp
https://www.mcaspets.org/

Conroe, TX,  Montgomery County Animal Shelter,  8535 Hwy 242,  936-522-3550
www.mcaspets.org

Corpus Chrisi TX,  Gulf Coast Humane Society,  3118 Cabaniss Parkway,  361-225-0845
http://www.gchscc.org/dogs

Corpus Christi, TX,  City of Kileen Animal Services,  2626 Holly Rd,  361-826-4630
http://www.cctexas.com/services/animal-services/adopt-pet
http://www.cctexas.com/departments/animal-care-services
https://www.facebook.com/corpuschristianimalcareservices/?rf=298039183689611

Corpus Christi, TX,  Focus on Forever (Corpus Chrisi Recue)
https://www.facebook.com/focusonfurever/photos/pcb.2066301586932054/206630132359

Cypress, TX 77429,  Animal ER of Northwest Houston,  27104 Hwy 290 West, #107,  281-304-0039
http://animalernwh.com/
http://www.animalernwh.com/contact.html
https://www.facebook.com/AnimalERNWH/

Deer Park Shelter and Adoption Center
4213 Luella Ave., Building G, Deer Park, TX 77536
Email: animalshelter@deerparktx.org
Phone: 281-478-7274
Website: https://www.facebook.com/DeerParkTX.AnimalShelter\

Dallas, TX,  214-535-3832
https://www.petstablished.com/public/search/shelter/75154#pets
https://www.facebook.com/DallasDogRRR
https://www.dallasdogrrr.org/

Dallas, TX,  SPCA Dallas (SPCA of Texas),  2400 Lone Star Dr,  214-742-7722
http://spcafindapet.com/AnimalName=&Species_1=Cat&Species_2=Dog&Species_3=Small%26Furry&PrimaryBreed=0&search=+Search+&ClientID=10&Species=All
https://www.spca.org/

Dallas, TX,  Dallas Animal Services,  1818 N. Westmoreland Rd,  214-670-8246
http://dallascityhall.com/departments/dallas-animal-services/Pages/default.aspx

Dickinson, TX,  Bayou Animal Services,  3120 Deats Rd,  281-337-3117
http://public.sheltermanager.com/animals/mt0943/
https://www.petfinder.com/shelters/TX2118.html
http://www.bayouanimalservices.org/
https://www.facebook.com/bayouanimalservices/

Texas Animal Control Solutions - Dickinson Chapter
3811 Dickinson Avenue, Dickinson, TX 77539
Email: shelterinfo@texasanimalcontrolsolutions.com
Phone: 214-513-8228
Website: http://www.texasanimalcontrolsolutions.com

Friendswood Animal Control
3000 W. Parkwood, (FM528) Under the water tower, Friendswood, TX 77546
Phone: 281-996-3390

Fulton, TX,  Humane Society - Rockport/Fulton,  1308 W. Myrtle St.,  361-729-8186
http://rockportfultonhumanesociety.org/

Galveston, TX,  Galveston Island Humane Society,  6814 Broadway St,  409-749-1919
http://www.galvestonhumane.org/adopt-today.php

Georgetown, TX,  City of Georgetown Animal Shelter,  110 W L Walden Dr,  512-930-3592
https://pets.georgetown.org/adoption/available-pets/
https://www.petfinder.com/pet-search?&shelter_id=TX34&sort=internal+desc
https://pets.georgetown.org/
https://www.facebook.com/GeorgetownAnimalShelter/

Granbury, TX,  Second Chance Farm,  PO Box 1085,  817-243-8172,  petharbor
http://www.secondchancerescuefarm.com/Availabledogs.html
http://www.secondchancefarmgranbury.org/
https://www.facebook.com/Second-Chance-Rescue-Farm-225551037503774

Grand Prarie, TX,  Grand Prairie Animal Services,  2222 W Warrior Trail,  972-237-8580
http://petharbor.com
https://www.gptx.org/city-government/city-departments/animal-services

Harker Heights, TX,  Harker Heights Pet Adooption Center,  403 Indian Trail,  254-953-5472
http://www.ci.harker-heights.tx.us/index.php/2011-11-22-17-14-10/petadoptioncenter
https://www.facebook.com/HHPetAdoption/

Houston, TX, Best Friends Animal Society -- found pets, housed at Pet Reunion Pavilion at NRG Arena, 1 NRG Pkwy, Houston, TX 77054
https://bestfriends.org/hurricaneharvey/lost-and-found-pets/nrg-pets

Houston, TX,  Adopt a Cat,  17319 Bamwood,  281-580-6652
https://adoptacattexas.org

Houston, TX,  Citizens for Animal Protection,  17555 Katy Fwy,  281-497-0591
http://cap4pets.org

Houston, TX,  Friends For Life,  107 E 22nd St,  713-622-5295
http://friends4life.org
Email: adoptionmanager@adoptfriends4life.org
Website: http://www.nokill1.org

City of West University Place - Animal Control
3826 Amherst St, Houston, TX 77005
Email: dparipovich@westutx.gov
Phone: 713-662-5831
Website: http://westutx.gov/286/Animal-Control

Houston, TX,  Homeless & Orphaned Pets Endeavor (HOPE),  PO Box 273331,  713-622-4673
https://www.homelesspets.net

Houston, TX,  Homeless Pet Placement League,  P.O. Box 273027,  713-862-7387
http://hppl.org

Houston, Tx,  Houston Humane Society,  14700 Alameda,  713-433-6421
http://www.houstonhumane.org

Houston, Tx,  Houston Pets Alive,  8620 Stella Link,  832-786-9310
http://www.houstonpetsalive.org

Houston, Tx,  Scout's Honor,  1302 Waugh Drive, Box 245 (Mail Only)
http://scoutshonor.org

Houston, TX,  Houston BARC,  Before Noon - 2700 Evella St After Noon, 3300 Carr St,  3-1-1 or 713-229-7300,  www.HoustonBARC.com
http://www.houstontx.gov/barc/
https://www.petfinder.com/pet-search?shelter_id=TX973
http://petharbor.com/search.asp?searchtype=ADOPT&friends=1&samaritans=1&nosuccess=0&rows=10&imght=120&imgres=thumb&view=v_animal&fontface=arial&fontsize=10&zip=77002&miles=20&atype=&frontdoor=1&stylesheet=include/default.css&shelterlist=%27HSTN%27
https://www.facebook.com/BARCHouston/

Houston, TX,  Harris County Animal Shelter,  612 Canino Road,  281-999-3191
https://www.facebook.com/HarrisCountyAnimalShelter/?sk=app%2F203351739677351%2F&app_data
www.Petharbor.com
http://www.countypets.com

Houston, TX,  Houston Humane Society,  14700 Almeda Rd,  713-433-6421
http://petango.com/
http://idogcam.com/humaneviewer.php?id=6
www.HoustonHumane.org

Houston, TX,  Houston SPCA,  900 Portway Dr,  713-869-7722
http://www.houstonspca.org/adopt/
http://www.houstonspca.org/adopt/harvey-rescues/harvey-found-dogs-beaumont.html
http://www.houstonspca.org/adopt/harvey-rescues/ 

Houston, TX,  Special Pals Animal Shelter in Houston,  3830 Greenhouse Rd,  281-579-7387
http://specialpalsshelter.org/project/dogs/
https://www.petfinder.com/pet-search?&shelter_id=TX115&preview=1
http://specialpalsshelter.org/
https://www.facebook.com/SpecialPalsShelter/posts/10155176045656743?hc_location=ufi

Houston, TX,  Citizen for Animal Protection,  17555 Katy Freeway,  281-497-0591
http://www.cap4pets.org/pet-adoptions
http://cap4pets.org/
https://www.facebook.com/cap4pets/

Huffman, TX,  LMN Feline Rescue,  P.O. Box 600
http://www.adoptapet.com
https://www.petfinder.com/member-pages/TX1279
https://www.facebook.com/LMN-FELINE-RESCUE-274192325966697/

City of Humble Animal Shelter
240 Dennis Street, Humble, TX 77338
Email: mlewis@cityofhumble.net
Phone: 281-881-1612
Website: www.cityofhumble.net

Ingleside, TX,  Ingleside Animal Control,  2078 Tiner Ln,   361-776-2531,   
http://petfinder.com
http://inglesidetx.gov/animal-control/
https://www.facebook.com/InglesideAnimalControl/

Irving, TX,  Irving Animal Shelter,  4140 Valley View Lane,  972-721-2259
http://www.ci.irving.tx.us/319/Lost-and-Found
http://www.cityofirving.org/130/Animal-Services

Katy, TX,  South Texas Animal Adoption Resource in Katy,  281-392-0927
http://staarnet.org

Kileen, TX,  City of Kileen Animal Services,  3118 Commerce Dr,  254-526-4455
http://www.killeentexas.gov/lost_and_found
https://www.killeentexas.gov/animals

Kingwood, TX,  Volunteers for Animal Protection, Humble,  P.O. Box 5266,  281-358-9818
http://vapadoptions.org

La Marque, TX,  Hurricane Harvey Animals of Galveston County,  1000 FM 2004 ,  281-910-1562
https://www.facebook.com/hurricaneharveyanimalsofgalvestoncounty/
https://www.facebook.com/hurricaneharveyanimalsofgalvestoncounty/?ref=br_rs

Lake Jackson, TX,  Brazoria County Humane Society,  141 Cana,  281-467-6300
https://spcabc.wordpress.com

Lake Jackson, TX,  SPCA Brazoria County,  141 Canna Ln,  979-285-2340,  www.facebook.com/SPCABrazoriaCounty
http://www.petfinder.com/pet-search?shelterid=TX571
https://www.facebook.com/SPCABrazoriaCounty

League City, TX,  League City Animal Shelter,  821 N. Kansas St,  281-554-1379
http://www.leaguecity.com/index.aspx?NID=92

Live Oak, TX,  Live Oak Animal Care and Control (Animals went to Best Friends),  8001 Shin Oak Dr,  210-653-9140
http://petharbor.com
https://www.liveoaktx.net/city-services/animal-care-and-control

Lufkin, TX,  City of Lufkin Animal Control,  1901 Hill St,  936-633-0218
http://petharbor.com/Harvey.asp
http://cityoflufkin.com/ac/

Lufkin, TX75902,  Friends at Kurth Memorial Hospital,  300 E Shepherd,  936-634-8881
https://www.facebook.com/Friends-At-Kurth-Memorial-Animal-Shelter-172348102782288/

Magnolia, TX,  Woodlands Dog Suites ,  9015 Shady Lane,  832-610-9900
https://www.facebook.com/woodlandsdogsuites/

Missouri City, TX,  Missouri City animal Shelter,  1923 Scanlin Road,  281-403-8707
https://www.facebook.com/mocityshelterpets/
http://www.erahvet.com/harvey-lf-pets.html
https://www.facebook.com/LOSTandFOUNDPETSofSETexas/
http://www.erahvet.com/harvey-lf-pets.html
https://www.facebook.com/Elm-Ridge-Animal-Hospital-178997993526/

WWEC Equine Evacuation Emergency
https://www.facebook.com/groups/363664037400458/permalink/370159010084294/

North Richland Hills Animal Shelter,  817-427-6570
PetHarbor.com

Pasadena, TX,  Pasadena Animal Control and Adoption,  5150 Burke Rd,  281-991-0602
https://www.petstablished.com/public/search/shelter/75154#pets
http://www.ci.pasadena.tx.us/default.aspx?name=animal_control
https://www.facebook.com/PasadenaAnimalShelter

Pearland, TX,  Pearland Animal Control and Adoption Center,  2002 Old Alvin Rd,  281-652-1970
http://petharbor.com
https://www.pearlandtx.gov/departments/animal-services
https://www.facebook.com/pages/Pearland-Animal-Control-Adoption-Center/843003692383714

Port Aransas, TX,  Port Aransas Animal Shelter,  409 W Cotter Ave,  361-749-5941
http://www.animalshelter.org/pets/
http://www.cityofportaransas.org/animal_control.cfm
http://animalfriendsofportaransas.org/
https://www.facebook.com/City-of-Port-Aransas-Animal-Shelter-610696435801307/

Rockport, TX,  Aransas County Animal Control,  872 Airport Road,  361-790-0151
https://www.facebook.com/Aransas-County-Animal-Shelter-397020817024040/
http://friendsofaransascountyanimalcontrol.org/index.php/check-here-for-lost-dogs/
https://www.facebook.com/Hurricane-Harvey-Lostfound-Pets-Of-Aransas-County-Tx-1653437044689634/
http://friendsofaransascountyanimalcontrol.org/
https://www.facebook.com/Aransas-County-Animal-Shelter-397020817024040/

Rosenberg, TX,  Fort Bend County Animal Services Shelter,  1210 Blume Rd,  281-342-1512
http://petharbor.com/search.asp?searchtype=LOST&start=3&friends=1&nopod=1&orderby=ID&rows=25&imght=150&imgres=thumb&tWidth=200&view=sysadm.v_fbnd&bgcolor=c5d1db&text=000000&link=852222&alink=852222&vlink=852222&fontface=arial&fontsize=10&col_hdr_bg=c5d1db&col_hdr_fg=000000&col_bg=FFFFFF&col_bg2=F1EFe2&col_fg=000000&SBG=c5d1db&zip=77469&miles=200&atype=&shelterlist=%27FBND%27
http://www.fortbendcountytx.gov/index.aspx?page=422

San Antonio, TX,  San Antonio Animal Care Services,  4710 TX-151,  207-207-4738
http://www.sanantonio.gov/Animal-Care/What-We-Do-Services/Adopt/Pet-Search
https://www.facebook.com/ACSAdoptablePets

San Leon, TX,  Bay Area SPCA,  3000 Ave R,  281-339-2086
http://bayareapetadoptions.org

South Houston, TX,  City of South Houston Animal Shelter,  207 Michigan St,  713-378-5788
https://www.facebook.com/SOUTHHOUSTON-ANIMALSHELTER/

Texas Litter Control
24950 Spring Ridge Drive, Bldg B, Spring, TX 77386
Email: adoptions@texaslittercontrol.org
Phone: 832-930-0228
Website: http://www.texaslittercontrol.org/

Sugar Land, TX,  Sugar Land Animal Services,  101 Gillingham ,  281-275-2364
http://sugarlandtx.gov/220/Animal-Services

Sugar Land, TX,  City of Sugar Land Animal Services,  101 Gillingham Ln,  281-275-2364
http://www.adoptapet.com/dog-adoption
https://www.sugarlandtx.gov/220/Animal-Services

Texas City, TX,  Galveston County Animal Resource Center,  3412 25th Ave N,  409-948-2485
http://petharbor.com/
http://www.gchd.org/animal-serivces/about-animal-services

The Woodlands, TX,  The Woodlands Animal Rescue,  24627 I-45 North,  281-681-7501
http://www.adoptapet.com/adoption_rescue/93408.html
http://www.woodlandsanimalrescue.com/

Tomball, TX,  Abandoned Animal Rescue,  419 E. Hufsmith Rd,  281-290-0121
http://www.aartexas.org

Waco, TX,  City of Waco Animal Control Services,  2032 Circle Road,  254-750-7082
http://www.waco-texas.com/animal-control.asp

Waco, Humane Society - Central TX Waco
http://humanesocietycentraltexas.org/view-dogs

Webster Animal Control
855 Magnolia, Webster, TX 77598
Email: atrover@cityofwebster.com
Phone: 281-316-3700

Louisiana:
New Orleans, LA,  The Inner Pup of New Orleans,  465 Lowerline,  N/A
http://www.theinnerpup.org/new-program-coming-soon--.html
https://www.facebook.com/theinnerpupofneworleans/

Lake Charles, LA,  Calcasieu Parish Animal Services & Adoption Center,  5500 Swift Plant Rd,  337-721-3741
http://cppj.animalshelternet.com/stray_search.cfm
https://www.facebook.com/Friends-of-Calcasieu-Parish-Animal-Services-Adoption-Center-514020402022090

Another list that lists more animal welfare groups across ALL TEXAS
https://drive.google.com/file/d/0B3Xikg6zupwITlRPV0tkZk1YUUk/view?ts=59ca8894

Facebook and other links- Texas

https://www.facebook.com/findtexasdogs
https://www.facebook.com/LostCatsTexas/
https://www.facebook.com/pg/LOSTandFOUNDPETSofSETexas/photos/?ref=page_internal

Another Chance RFT
http://anotherchancerft.org/

German Shepherd Photos (Hurricane Harvey LOST & FOUND Pets & Foster Offers - Houston) https://www.facebook.com/photo.php?fbid=10208031411342998&set=gm.1422506351203185&type=3&theater&ifg=1

Gilligan's German Shepherd Rescue,  409-790-3508
https://www.facebook.com/GilligansRescue/

Guardian Pitbull Rescue
ttps://www.facebook.com/pg/GuardianRescue/photos/?ref=page_internal
https://www.facebook.com/GuardianRescue/?fref=gc&dti=515022888841691&hc_location=ufi

Texas Flood Pets
texasfloodpets.com

South Texas Shelter Dogs,  410-608-2195