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.
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.
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. Those with lower income or long unemployment will get priority if they apply by March 8. You can take part in the program whether or not your landlord participates. They can even help with late fees you may owe. Apply now while funds are still available.
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.