I think eating food while hungover is something that people only do when they're half-assing it. What you need is to drink your own damn tears. Cry into a coffee mug, DRINK IT. Become stronger through your pain.
I drink a lot of gentle tea, like jasmine green or unflavored white teas, and my only food is pain medication, because my migraines are true and I am too weak for real food when alcohol sick.