• https://rehome.adoptapet.com/
• https://www.facebook.com/groups/houstonadopt/
• http://nextdoor.com/
• https://www.howimetmydog.com/
• https://pet-net.net/rehome-a-cat/

There are more re-homing websites you can locate on the internet.  Bringing your animal to the shelter should be your last resort.  

• https://www.apartmentguide.com/apartments/Texas/Houston/pet-friendly-4lh/
• http://www.zillow.com/houston-tx/pet-friendly/
• https://www.abodo.com/pet-friendly

Having hard times and need financial assistance  https://friends4life.org/get-help/financial-issues/