This is a good idea. If you don't want to share specific details, then give them a note from your university's disability services that lists (i) that you're registered with them, and (ii) accommodations that you qualify. This will be just as effective. Your professors will understand that you have a lot on your plate.

I have a note from disability services. I have chosen not to disclose my exact medical details to my professors, but I do tell them when I'm "sicker" than usual. Sometimes when I have severe side effects from medication, etc. I'll get a note from my psychiatrist and psychologist and share that (alongside my concerns) with my dean. He will either write to my professors, or help me work out how to approach professors.

This was really helpful during finals last semester, when my mood stabilizer pretty much sedated and disoriented me in the morning. I was able to reschedule my exams to the afternoon.