I have a little bit similar situation. My son is on a gluten-free diet (no wheat, no bread, no sweets, no cookies, etc). He is 3 years old. If you know what does it mean a gluten-free diet, you can imagine the "variety" of foods I could offer him. There are periods when he just does not wish to eat that food, but I try to have at least 2 dishes (to be able to offer the other dish if the first one doesn't work). However, if he does not eat anything, he remains hungry, for some period, but later I know he will eat. He could eat a little in the morning, and that's all. At the start it was killing me, but now I know he will eat when he wants.
You know, once I've met a woman whose son was on this diet too, but he also was allergic to fruits and vegetables. I've asked her about how is she dealing with all these difficulties? The only thing she replied was: "What should I do? I wish and I must help him".
Just imagine that eating healthy is a vital necessity, not just your or doctor's wish. Think and hope you will find the way. Moreover it is time to do something now, when it is possible.