Approach the question individually: no strength - don't go, if you have strength - run. Do not forget to eat something quickly digestible and not heavy before training (30-60 minutes), because you need to draw strength from somewhere, they will not be taken from the air, but glucose in your blood will help you a lot. From personal experience: despite a 3-hour sleep, I went to workout (morning jog with weights + standard exercises), because I felt fine, and in the end it went off with a bang, then I came home, took shower and just went to bed. I was proud and felt energetic all day. Conclusion: proceed from personal feelings.
It's definitely worth giving up. Your body is exhausted, it must recover. Running will take away strength and energy from you, which are not already there, and besides, the organs will work to wear and tear. Once, of course, it won't come around much, but still. And what is the goal? ..
Don't ruin your health. Get enough sleep - run.
If jogging for you initially does not bring strong discomfort, let's say this is your ritual for several years, a good breath, then I think 10-15 minutes will not hurt, but on the contrary will tone you up. It's another matter if initially this is a big test, you cannot run 300 meters and after it you feel discomfort, then it is better not to take risks. Especially if there is a busy day ahead, and not wallowing on the couch. In any case, I would have raised carbohydrates in front of her and especially after her and would have eaten a hearty meal in order to recover better.
Look at your condition, because physical exercise is not so much tiring as, on the contrary, it gives a charge of vivacity, so maybe this is not a bad idea at all, but I would rather recommend a simple walk on foot so as not to overload the body. If you feel tired, it makes sense to take a break and skip a workout, and if you feel you can and want to run - why not.
it depends what the night was) if you, well, I don’t know, unloaded the carriages tirelessly and without closing your eyelids - then, of course, you should refuse, otherwise you will fall off somewhere. but if you were busy with relatively quiet things - reading there, watching movies / videos, communicating or some small everyday life - in the spirit of washing dishes, then it is unforgivable to refuse an invigorating run. Depends, of course, on the weather and the degree of lighting, but the most beautiful thing is to run from 4 to 6 in the morning. Besides, it will help to hold out during the day, if the next night for some reason should be "sleepy")