My endo was willing to help me do whatever I wanted to do in order to feel better with or without a letter. HOWEVER, I was and am also seeing a licensed psychiatrist, and my endo knew that. And my psychiatrist did write my endo a letter. A psychiatrist is a therapist who has obtained unto the level of PhD. Basically, she is a licensed physician. In my opinion, you need to find a psychiatrist. An easy way to make sure the person you plan on seeing is a psychiatrist is to ask their receptionist, "can he or she perscribe me medicine?" If the answer is yes, then all should be fine.
I also believe you need a licensed psychiatrist to write you your GID letter.