Absolutely.
Stress can do all kinds of things to your body. It can lower the strength of the immune system letting all kinds of things in. Unusual and irregular sleeping patterns can mess with your metabolism and change the way your energy is processed. Sleep is something that you need to stay healthy. Stress is also something that seeds itself and most of the time you won't notice until you end up breaking out or experiencing a panic attack.

The situation you've described (your exams and how the issue comes up while you're doing related things) really sounds like a stress related issue to me, the anxiety is possibly causing spikes of blood pressure fluctuation. See how you go once you're on-top of your study situation, if it's all over and you're still experiencing the discomfort then I'm going to guess it's an internal problem that you will probably need some antiseptic drops and a little ibuprofen for.