Too ill for university exams

Last Tuesday I started having severe pain in my wisdom tooth and saw that my gum had detached from the side of my molar, leaving a gaping hole to the root.
I woke up Wednesday morning feeling extremely ill so I went to the dentist who told me that the tooth was impacted. He referred me to the dental hospital to have it removed (which may take three months).

By Saturday, the pain and feeling of being really ill had got a lot worse, so I returned to the dentist. He told me the wisdom tooth had now become infected and put me on some antibiotics and painkillers.
Since Saturday I have never felt more ill in my life. Constant headache, throwing up, sweating, being lightheaded and dizzy whenever I stand/walk that I end up tripping up, things feel very heavy (ie: doors), and sleeping a LOT.
I went back to the dentist today to be told that the infection had not cleared up, and may have spread to my ears and beyond. He's put me on some new antibiotics.

The only problem is, I have exams tomorrow, Saturday and Tuesday! I don't know if I can make it into the exams because I'm in so much agony and feel like I'm going to faint whenever I'm not in bed. I also missed my coursework deadline on Monday. I had the coursework done, but being so ill it was the last thing in my mind so I forgot and the submission link has now been removed.

What are my options? Am I ill enough by university standards to be able to sit the exams later on in the year? If so, should/can I get a letter from the dentist? Should I have gone to my GP instead? I read that they refuse to deal with dental problems. Should I go to my exams and fail them, or just not turn up?

Sorry for the long post, I don't know what to do and I don't want to get thrown out of university..