You should apply for any rent assistance that you may qualify for. Keep records to prove you applied. If you cannot get help with rent and need to use the CDC moratorium, you may need to prove that you applied for all help available.
You can apply with more than one program. Note that you can only get one rent assistance payment per month. If you apply to two different programs and both give you help for the same month, you will have to pay one back right away.
Many local programs are older and more established than the statewide Texas Rent Relief program. That means local programs may be better at getting you funds more quickly. Some local programs may not be able to help with as many months of rent, though.
Rent Assistance: Texas Rent Relief and Local Programs
1. If you are behind on bills, go to Texas Rent Relief and apply for up to 15 months' worth of rent and utilities. You can take part in the program whether or not your landlord participates. They can even help with late fees you may owe. Private and public housing tenants are eligible. Apply now while funds are still available.
2. Apply to any local rent assistance programs. You can find partial lists of local programs here and here and through the CFPB's lookup tool. Programs change and lists get updated as money becomes available, so none of these lists are likely to be 100% complete. Be sure to check each of them!
3. Go to your city and county websites. Many local governments help with rent. For example, the Houston-Harris County Emergency Rental Assistance Program.
Note that some programs require landlord participation. Others do not.