When you are tired, ill, emotionally wrecked, or physically traumatized, but feel taking time off will put you so far behind that you’ll be even more stressed and tired, see if it’s possible to (a) make yourself more comfortable, and (b) work in tiny chunks.
(A) Sitting at your desk in a normal chair might be too much, but perhaps you can work in a recliner, on the couch, or in bed. Maybe even typing on a laptop is too much, but it might be possible to take marginal notes on a book, to be typed up later. Wear your owl pyjamas and fluffy slippers. Assemble pillows and heating pad (or ice water and fans, depending on the season).
(B) Then work in increments of 10-15 minutes, with 10-15 minute rest periods after each work session. Obviously this is not good for those big problems that need 3 hours of clear head time, but you’re not going to be trying to do those anyway when you’re sick/tired/traumatized. OTOH it is very possible to do half a day’s work in a full day by this work-rest pattern, reading, taking notes, grading, editing, writing half a paragraph at a time, and then you’re not so terribly behind. It is important to rest, really rest, between these little sprints, and not do things that will suck you into procrastination mode. Small household tasks (not a big clean-up project) are also appropriate breaks from the work if you have the energy. The point is to do something that does not involve a screen or a page.
And remember that the best is the enemy of the good.