In the State of Texas if your doctor has certified your dog as an emotional support animal then your dog would be allowed to stay with you regardless of community policies. You would need to complete a lease addendum taking financial responsibility for your dog. In addition pet fees, rent, and deposits are traditionally waived.
The exception would be if your dog has any sort of bite history. In that case a landlord could deny your animal.
Generally speaking you need to have your ESA letter renewed annual by a physician. There are scam services online claiming a lifetime designation. Don’t waste your time or money on them.
This is not to be taken as legal advice. Consult your physician or an attorney for details on emotional support animals.