Have you ever been really tired when all you've done is attend pointless meetings where you did not have to do very much, or wait for a plane, or wait around for other people to do things so you can complete the next step of a process? You can expend energy in those activities; you might even call them work, if they are part of your day at work and more or less mandatory. You are tired afterwords, yet you did not even try to get anything done. You are not tired from working, but from not working, which is extremely wearisome. You could say: "I did not work very hard today, and as a consequence I am very tired."
In contrast, you might write for two hours first thing in the morning and not feel tired at all. If you are doing it right, you might have even more energy for the rest of the day to go out guiltlessly and do other things unrelated to your writing. It might sound like heresy, but you do not need to be mentally fatigued and emotionally spent after writing for a few hours.
If you sleep well, then you will be well-rested and be ready to write the next day. There is no point in bragging about how over-worked you are, so much that you are losing sleep. That's like boasting about not being able to work, since chances are that your work after an unrestful night will not go as well. When I am sleep-deprived I barely get through the day, through the classes I have to teach, and nothing more. Nothing to brag about.
A related point:: if you exercise for an hour, you will more energy, rather than less, the rest of the day. The exercise will not tire you out physically the way waiting in an airport will. Fatigue comes more from not exercising or from overdoing it. After exercising, rest is more restful.