You can appeal the UI denial, and you should. But there's a time limit---don't know exactly how long, maybe 30 days, maybe more---so you'll want to get it done ASAP. This is where you need to get documentation from your pdoc, and therapist if you have one, as to your mental state and difficulty "playing well with others" so to speak. These are mitigating circumstances, and they could make a difference because the firing was due to factors related to your disability.

It's a long shot, to be sure, but you've got nothing to lose by trying. In the meantime, I'd file for SSDI yesterday, even though denial is likely. But I wonder, can you not get veterans' benefits? You are indeed partially disabled by your illness.....seems like there's something the VA could do.