Felt, I definitely do this too. I know it's not the healthiest but I call it looking on the bright side of things, lol.
But I get it, because I definitely have my moments where I just survive off iced coffee, air and whatever gasses are in my body. Despite not having an appetite, do you think it would be possible to eat lighter foods? Things that wouldn't take you very long to eat and that wouldn't make you feel super full. Like maybe a small bowl of oatmeal in the morning, a salad with a few pieces of meat for dinner, or some wedges/pieces of fruit throughout the day/for lunch. It may be hard to do, but maybe eating at least a little bit will help you deal with the challenges at work.
There are also those meal replacement shakes, like Ensure, that you can chug down from time to time just for the energy and nutrients! Those get me through a lot of days. Electrolyte water, too. But food is still a better option, I think; it's just that food can be so hard to eat and keep down when you're stressed.