Oh I get sick all the time, so I feel ya. I have learned that no matter how sick I feel, I HAVE to eat. And actually I've also learned to eat very regularly, before I'm hungry. If I eat once my tummy tells me I'm hungry, I'll puke. it's a vicious cycle actually!
I call myself a hobbit... if you google the wikipedia definition and read how many times a day they eat, you'll understand!
So try to eat every two hours, small healthy meals, and see if that helps. It was really hard for me to do this since I'm used to eating 2-3 times a day and ONLY when I'm hungry, but honestly it has helped so much.