Will my Professor tolerate this medical excuse again?
Go to the hospital NOW and worry about the exam and your professor later.

If you tell your professor that you had to go to the hospital, she'll most likely just accept that. Of course, you can ask for that note nevertheless, just in case. 

Once you are ok again, think about how you can reduce stress and get enough sleep regularly. On the long run, constant lack of sleep and stress will hurt you (even more than it already did so far).