Okay so your doctor is sketchy as fuck. I would email the doctors office and have them put it in writing as to why she won’t write the note. Something like “ as per my conversation with Doctor such and such, he/she said that they would not be willing to write me a note verifying and and supporting my need for an ESA due to have no previous experience, writing a letter for that purpose and unwillingness to go to court and the verify information.”
She just messaged me back, and said that no other provider willing to do it for me, because it’s entirely up to my provider if she is comfortable and willing to write me a letter. I had two fucking appointments with her today, and she charged me $500, just to be told that she’s not comfortable.