It really depends on your university, and particular your own department's, rules on these things. As Saber said earlier, you might not be able to get any supporting medical evidence, because some doctors are quite strict like that and any long-term conditions like the ones you cited should have been registered at the outset, or at the very least before your exams started.
That said, I hope you are able to get your circumstances taken into consideration. But no one on here can really advise without knowing the uni and department.
Everything relating to this should be in your departmental handbook. That will give you a far better indication of your chances of getting your health taken into consideration, than anyone on here can