Doctors don't charge for a doctors/sick note (as far as I know) but they may charge for letters, which take longer for them to do (I think it depends on the doctor if they charge or not.)
It is probably worth you going to see your doctor and explaining what is happening. It would probably also be a good idea to see you tutor at uni and explaining the circumstances you have at the moment. They should then take that into account with exam results etc. It will probably help as well if you are struggling with coursework or can't get to lectures etc all the time.
Most lecturers are fairly helpful once they know your circumstances, some aren't, but theres not a lot that can be done about that!!
Just try and make people aware of it, if you are ok with that so that they will probably give you more lee-way with things.