The ADA Amendment of 2008 expanded the "major life" definitions. So lets not get uptight over the word "major." They are now very liberal. Secondly, the claimant does not have to prove their disability. The employer has to disprove it. That's why there is discovery.
IMO, I would file a claim with EEOC and let them investigate. Start shopping for a lawyer specializing in ADA claims. There are plenty.