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

Austin, TX,  Austin Pets Alive,  1156 W. Cesar Chavez St,  512-961-6519


Alvin Animal Adoption Center - c/o Alvin Police Department
550 W SH 6, Alvin, TX 77511
Phone: 281-388-4331

Angleton, TX,  Brazoria County Animal Control,  3602 County Rd 45,  979-864-2265

Angleton Animal Control Adoption Center
535 S. Anderson, Angleton, TX 77515
Phone: 979-849-9550

Aransas Pass, TX,  SPCA San Patricio County (Sandra Sue Benson Shelter),  4630 FM 1069,  361-332-1445

Austin, TX,  Austin Humane Society,  124 Anderson,  512-646-7347

Austin, TX,  Austin Pets Alive,  1156 W. Cesar Chavez St,  512-961-6519

Austin, TX 78702,  Austin Animal Center,  A, 7201 Levander Loop,  512-978-0500,

Bay City, Matagorda County Shelter (Fairgrounds/Bay City)

Baytown, TX,  Baytown Humane Society,  P. O. Box 2772,  281-424-3103

Baytown, TX,  Baytown Animal Services,  705 N Robert C Lanier Dr,  281-422-7600

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

Beaumont, TX,  Humane Society - Southeast TX,  2050 Spidletop Ave,  409-833-0504

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

Buna, TX,  Buna Animal Hospital Drs. Foster,  34299 Highway 96 South,  409-994-5986

Carthage, TX,  Carthage Panola County Pound,  1024 US Hwy 59 N,  903-693-2877

Carthage, Chris Guard

Clear Lake and League City, TX,  Second Chance Pets,  281-286-3535

Cleveland Animal Control
226 Peach Street, Cleveland, TX 77327
Phone: 281-592-2621

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

Conroe, TX,  Montgomery County Animal Control,  8535 Hwy 242,  936-442-7738

Conroe, TX,  Conroe Adoption Center (Montgomery County Animal Shelter),  8535 Hwy 242,  936-522-3550

Conroe, TX,  Montgomery County Animal Shelter,  8535 Hwy 242,  936-522-3550

Corpus Chrisi TX,  Gulf Coast Humane Society,  3118 Cabaniss Parkway,  361-225-0845

Corpus Christi, TX,  City of Kileen Animal Services,  2626 Holly Rd,  361-826-4630

Corpus Christi, TX,  Focus on Forever (Corpus Chrisi Recue)

Cypress, TX 77429,  Animal ER of Northwest Houston,  27104 Hwy 290 West, #107,  281-304-0039

Deer Park Shelter and Adoption Center
4213 Luella Ave., Building G, Deer Park, TX 77536
Phone: 281-478-7274

Dallas, TX,  214-535-3832

Dallas, TX,  SPCA Dallas (SPCA of Texas),  2400 Lone Star Dr,  214-742-7722

Dallas, TX,  Dallas Animal Services,  1818 N. Westmoreland Rd,  214-670-8246

Dickinson, TX,  Bayou Animal Services,  3120 Deats Rd,  281-337-3117

Texas Animal Control Solutions - Dickinson Chapter
3811 Dickinson Avenue, Dickinson, TX 77539
Phone: 214-513-8228

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

Galveston, TX,  Galveston Island Humane Society,  6814 Broadway St,  409-749-1919

Georgetown, TX,  City of Georgetown Animal Shelter,  110 W L Walden Dr,  512-930-3592

Granbury, TX,  Second Chance Farm,  PO Box 1085,  817-243-8172,  petharbor

Grand Prarie, TX,  Grand Prairie Animal Services,  2222 W Warrior Trail,  972-237-8580

Harker Heights, TX,  Harker Heights Pet Adooption Center,  403 Indian Trail,  254-953-5472

Houston, TX, Best Friends Animal Society -- found pets, housed at Pet Reunion Pavilion at NRG Arena, 1 NRG Pkwy, Houston, TX 77054

Houston, TX,  Adopt a Cat,  17319 Bamwood,  281-580-6652

Houston, TX,  Citizens for Animal Protection,  17555 Katy Fwy,  281-497-0591

Houston, TX,  Friends For Life,  107 E 22nd St,  713-622-5295

City of West University Place - Animal Control
3826 Amherst St, Houston, TX 77005
Phone: 713-662-5831

Houston, TX,  Homeless & Orphaned Pets Endeavor (HOPE),  PO Box 273331,  713-622-4673

Houston, TX,  Homeless Pet Placement League,  P.O. Box 273027,  713-862-7387

Houston, Tx,  Houston Humane Society,  14700 Alameda,  713-433-6421

Houston, Tx,  Houston Pets Alive,  8620 Stella Link,  832-786-9310

Houston, Tx,  Scout's Honor,  1302 Waugh Drive, Box 245 (Mail Only)

Houston, TX,  Houston BARC,  Before Noon - 2700 Evella St After Noon, 3300 Carr St,  3-1-1 or 713-229-7300,

Houston, TX,  Harris County Animal Shelter,  612 Canino Road,  281-999-3191

Houston, TX,  Houston Humane Society,  14700 Almeda Rd,  713-433-6421

Houston, TX,  Houston SPCA,  900 Portway Dr,  713-869-7722 

Houston, TX,  Special Pals Animal Shelter in Houston,  3830 Greenhouse Rd,  281-579-7387

Houston, TX,  Citizen for Animal Protection,  17555 Katy Freeway,  281-497-0591

Huffman, TX,  LMN Feline Rescue,  P.O. Box 600

City of Humble Animal Shelter
240 Dennis Street, Humble, TX 77338
Phone: 281-881-1612

Ingleside, TX,  Ingleside Animal Control,  2078 Tiner Ln,   361-776-2531,

Irving, TX,  Irving Animal Shelter,  4140 Valley View Lane,  972-721-2259

Katy, TX,  South Texas Animal Adoption Resource in Katy,  281-392-0927

Kileen, TX,  City of Kileen Animal Services,  3118 Commerce Dr,  254-526-4455

Kingwood, TX,  Volunteers for Animal Protection, Humble,  P.O. Box 5266,  281-358-9818

La Marque, TX,  Hurricane Harvey Animals of Galveston County,  1000 FM 2004 ,  281-910-1562

Lake Jackson, TX,  Brazoria County Humane Society,  141 Cana,  281-467-6300

Lake Jackson, TX,  SPCA Brazoria County,  141 Canna Ln,  979-285-2340,

League City, TX,  League City Animal Shelter,  821 N. Kansas St,  281-554-1379

Live Oak, TX,  Live Oak Animal Care and Control (Animals went to Best Friends),  8001 Shin Oak Dr,  210-653-9140

Lufkin, TX,  City of Lufkin Animal Control,  1901 Hill St,  936-633-0218

Lufkin, TX75902,  Friends at Kurth Memorial Hospital,  300 E Shepherd,  936-634-8881

Magnolia, TX,  Woodlands Dog Suites ,  9015 Shady Lane,  832-610-9900

Missouri City, TX,  Missouri City animal Shelter,  1923 Scanlin Road,  281-403-8707

WWEC Equine Evacuation Emergency

North Richland Hills Animal Shelter,  817-427-6570

Pasadena, TX,  Pasadena Animal Control and Adoption,  5150 Burke Rd,  281-991-0602

Pearland, TX,  Pearland Animal Control and Adoption Center,  2002 Old Alvin Rd,  281-652-1970

Port Aransas, TX,  Port Aransas Animal Shelter,  409 W Cotter Ave,  361-749-5941

Rockport, TX,  Aransas County Animal Control,  872 Airport Road,  361-790-0151

Rosenberg, TX,  Fort Bend County Animal Services Shelter,  1210 Blume Rd,  281-342-1512

San Antonio, TX,  San Antonio Animal Care Services,  4710 TX-151,  207-207-4738

San Leon, TX,  Bay Area SPCA,  3000 Ave R,  281-339-2086

South Houston, TX,  City of South Houston Animal Shelter,  207 Michigan St,  713-378-5788

Texas Litter Control
24950 Spring Ridge Drive, Bldg B, Spring, TX 77386
Phone: 832-930-0228

Sugar Land, TX,  Sugar Land Animal Services,  101 Gillingham ,  281-275-2364

Sugar Land, TX,  City of Sugar Land Animal Services,  101 Gillingham Ln,  281-275-2364

Texas City, TX,  Galveston County Animal Resource Center,  3412 25th Ave N,  409-948-2485

The Woodlands, TX,  The Woodlands Animal Rescue,  24627 I-45 North,  281-681-7501

Tomball, TX,  Abandoned Animal Rescue,  419 E. Hufsmith Rd,  281-290-0121

Waco, TX,  City of Waco Animal Control Services,  2032 Circle Road,  254-750-7082

Waco, Humane Society - Central TX Waco

Webster Animal Control
855 Magnolia, Webster, TX 77598
Phone: 281-316-3700

New Orleans, LA,  The Inner Pup of New Orleans,  465 Lowerline,  N/A

Lake Charles, LA,  Calcasieu Parish Animal Services & Adoption Center,  5500 Swift Plant Rd,  337-721-3741

Another list that lists more animal welfare groups across ALL TEXAS

Facebook and other links- Texas

Another Chance RFT

German Shepherd Photos (Hurricane Harvey LOST & FOUND Pets & Foster Offers - Houston)

Gilligan's German Shepherd Rescue,  409-790-3508

Guardian Pitbull Rescue

Texas Flood Pets

South Texas Shelter Dogs,  410-608-2195