YES YES YES!
Food is an integral part of contributing to anxiety. I was leading a very healthy lifestyle about 2 years ago (no meat, fruits, veggies, no processed foods or sugars, limited caffeine) and I felt GREAT! I still had anxiety, but it wasn't beyond the scope of what I would consider "normal".
More recently I am back in school and working, and eating really terrible foods (along with drinking coffee and smoking cigs) this is BAD!
I have seen a big increase in my daily anxiety and it's gotten to the point where I've decided to change my diet again and eat the right things. It really can and will make a difference.
about the anxiety/food allergies: my mom showed me an article that did, in fact, relate food allergies to anxiety. So might be something to look in to