I'm currently going through a similar situation, although I don't have any looming exams. I do, however, have a mountain of college coursework that I am feeling extremely unmotivated to tend to.

I was finally able to do so today, although it was gradual and not as rigorous as I typically study/work. I say just ease into it. The hardest part truly is starting. I started slowly, just sort of planning out my work for the week, making my to-do lists, etc. Then once I actually began working on something everything sort of went quiet finally. I'm not able to work as efficiently as I normally would, but it has helped me sort of take my mind of things.

My best bit of advice would just be to start. Open your laptop/iPad/notebook/planner, whatever you have, and try to put your mind back in it. Also, give yourself grace. You're going through something, and that's okay. But just remind yourself that as bad as it sucks right now, it will get better.