If you tell your employer about your mental illnesses and the treatments you're in, there's a good chance you'll be demoted to a position you don't want or fired. The exception is if your employer is incredibly nice. Do keep in mind though, if you ask for a reference, your employer may state you were offered a promotion but declined because you explicitly stated you didn't think you could handle the job. It isn't going to look very good.

I would say to accept the promotion and look at the new position as motivation to improve your abilities to cope with stress.