(urgent) HOA denied my doctor's ESA (emotional support animal) letter - because it's for 3 chickens [NC]

I know it sounds ridiculous, but I've got a mental health history, and ever since I bought chickens last year, my anxiety has plummeted.

Hurricane destroyed our rental last Fall, so we had to make a snap decision to move - and bought a house in an HOA and "no poultry" rule (there were VERY few options at the time).

My primary physician happily wrote me an ESA letter - it's very valid: I work from home, often outside hanging out with the birds, who keep anxiety and panic attacks at bay

Welp, two wandered too close to a neighbor's house and "disappeared" (we're on an acre, btw), and now I'm in trouble. After a phone call and my feeble attempt to defend myself, she simply said I had to get rid of them, citing something generated from AI that supported her side.

I was literally planning on picking up more tomorrow (obviously, I wouldn't free range them anymore).

And I don't know how badly I want to fight - though I LOATHE the injustice.

On one hand, my anxiety has improved enough on its own, and my partner was planning on taking a job that - frustratingly - would have us relocate by Fall or sooner. The "easy" answer is to wait it out and just get more then, if I can. But what if panic attacks return?

On the other, I've been a miserable wreck without my girls and need to figure out NOW what to do with the last one. Not to mention, with "bird flu," the cost of chicks and chickens has skyrocketed (if you can even find any!), and I don't want to worry about what prices will look like by then, either.

Is this worth the fight? I don't want to agonize over 6-8 months at this house.

Thanks much in advance!

***To add: The biggest problem, legally, is that she's a newer doctor for me, and it was the old one who originally diagnosed me and recorded instances of my then-panic disorder. Idk if that's relevant, but the ESA doc has only taken my records and testimony.