Remember that your health comes first. While a career in medicine might be at the top of your list, you need to make room for physical and mental care. And remember that as you proceed through it, a pre-health curriculum is only going to get tougher.
This being said, I do not think that mental illness is always an immediate roadblock. I rely on counseling appointments to get through school with social anxiety and depression -- it's not easy, but it's doable. No one on this forum is going to be familiar with your specific circumstances, however.
Does your school have a wellness center? Is there anyone you can contact that can put you in touch with a counselor, a medical doctor, a relevant organization, etc.? I would definitely see what your options are first -- including whether those options will help or hinder you -- and go from there. And always remember that dropping out due to mental or physical strain is not a sign of weakness or failure; you're looking out for yourself, and that's the most important thing.
Best of luck.