Can you do this without citing your mental health needs? Maybe, but probably not. If you can get your regular doctor to consult with your mental health professionals and cite physical needs, then you could possibly skirt the issue.
Since you are dealing with a hostile boss, I'd say that there is no way to get around the fact that you have mental health issues that need to be addressed directly.
This sounds like you may be in a position where you need to go to HR.
If you go to HR, be ready with notes from a doctor and a brief description of the medical necessity of time off. HR IS NOT YOUR FRIEND so be sure that you have everything in perfect order. Keep records of what you told them and send them a follow up email. Print out that email, and take it home with you.
If your boss is using your disabilities against you, it is imperative that HR knows about any problems you are having with those disabilities. HR's interest is in defending the company against threats. Once they know you have disabilities, then anyone who bothers you after that point becomes the threat to the company.
If you can get a doctor to write you a note saying that you need time off, that would be the best approach. Since you are in the USA, if it's that serious, you may want to put in for short-term disability.
While you are out, you should seriously consider updating your resume and finding a less hostile work environment. No job is worth your health.
Try to work with HR on this, but don't complain about your boss to them if you haven't already established that you have health issues or HR may interpret that as trying to cause trouble. You are in a difficult position, so be careful