Don't listen to people on this thread talking about "at-will employment", which (1) doesn't really apply to contractors and (2) doesn't apply to most discrimination cases, which are covered by separate laws (ADA, the Age Discrimination act, FMLA, etc).
Contractor status is one of those things you can often actually contest. Your employer referring to you as an "employee" is probably not dispositive, but there are a bunch of other tests (how much control you have over your work, etc) that an employment lawyer can walk you through.
Flip side of this: if your former employer is big and well-known, chances are they're well aware of the legal tripwires for contractors (everyone is after Microsoft infamously blew up over misclassification). Your actual contract, the one that actually got signed, probably spells out in great detail the fact that you are not a full-time employee entitled to benefits. So if it's a clueful company, it may be a steep hill to climb to argue that you were misclassified.
Terminating an employee with no previous disciplinary record right after a mental health crisis would be sketchy pretty much everywhere in the US, and most employers would be worried about legal repercussions. So it's possible that if you get a decent lawyer, you might be able to put together a nastygram that will get your former employer to cough up a settlement of some sort, rather than going to bat over your contractor status, which would be expensive for everyone.
Best of luck.