It kind of depends on what you mean by SEVERE mental illness.

Yes, you can become a doctor with MI.

But severe MI.. well. Again it depends on what you mean by that. I think for you, you should seek council from school advisors, a therapists, or people in the medical field. explain your challenges and see what they think about your options and possibilities. I don't know how severely mentally ill you are. when someone says severe MI it implies a pretty critical state.