I've had this problem before. First, if children don't eat when they're sick, doctors and the books say don't worry! Even when we're sick, it's healthy to eat but we may lack the appetite. It's hard to impress on children to eat when they don't feel like it, so don't worry.
After children are sick, they tend to get spoiled. My son goes through this after every time he's sick. I coddle him, hold him, pay 100% attention to him, etc. My son also went through a stage when he only ate junk food and meat. No veggies and fruits. How I broke him is that I didn't feed him any junk food, only meat, veggies, fruits, and rice. At first, he wouldn't eat it. Sometimes he would shove hiw bowl and scream. I would take his bowl away and tell him not to eat, and act like I was eating his food. The first few times, he didn't care. But then he got hungry. After a while, he would eat, spit it out, and then I would go through the whole charade of taking away his food, telling him not to eat, and act like I was eating it. This worked for me. It took a while, I would say 3 or 4 days before I happily began eating healthy food. Despite all the energy that went into it, it was definitely well worth it b/c he went back to eating healthy food.