Generally, having exams or difficulty at work (long hours) is not an excuse for not fasting. Either they must be patient and hang in there or try to have their exams postponed or taken earlier.
Generally, one who is ill qualifies to not fast while she is ill as it is one of the acceptable excuses.
however, in your case it's a mix of the two above. Although being ill, you mentioned you are able to fast. But adding exams burden will make you further ill and cause more harm. IF fasting alone was going to cause you harm and make you more ill then you would be excused but if it's the exams then I believe any shaykh will tell you to have your exams rescheduled at another time. That's my opinion and understanding on the matter. But for a definitive answer i would ask a shaykh. Here's one you can ask:
sheikh at Huda TV | 002 02 38555 248 9 | firstname.lastname@example.org