My Tatiana has been designated as a service/emotional support animal by my doctor. He did it with a letter, which I show people. So far, Tatiana has gained access with no problems. Incidentally, I have Tatiana in a purse/pet carrier. Perhaps that's why people were lenient about granting Tatiana access?
As far as Tatiana gaining access to a medical facility, my doctor wrote out A PRESCRIPTION (like off his prescription pad) for Tatiana to be allowed in the hospital with me. However, this was at the hospital he practiced at. I have not visited other hospitals (yet). I don't know if his prescription would work at other medical facilities. Incidentally, my doctor is a very important doctor at his hospital. The staff (and security guards) take one look at the prescription (with my doctor's name, license #, etc), and Tatiana is granted access, no questions asked. It helps if your doctor has clout.
I hope this helps.