What can you do about being fired for a disability in an at-will state?

This is something I've thought about recently as I was fired from a job a few months ago. I was fired because I missed a lot of work, and my last day I told my boss I needed to go ahead and leave because I needed to go back to the hospital, and I was fired. Being manic at the time, I didn't really care. But seeing as it's an at-will state, and their reasoning was I had missed a lot of work (with no doctors excuses or anything), i'm just kinda wondering how that even works. How do you even prove they fired you for something related to your disability? If you're in an at-will state, couldn't they just make up some random reason unrelated to your disability so that you can't do anything? 🤷🏻‍♀️ I asked for reasonable accomodations and they said no.

Anyway, I don't plan on doing anything about it simply because I have a new job and I'm also depressed and don't care to go through the hassle. But it just kinda feels like the ADA means absolutely nothing if your state is at-will.