When you end up with a disease like this it really exposes our blind spots in medicine. I even somewhat resent that doctors didn't identify this in me when I was young. It was 23 years of sinus headaches until a girlfriend did the research and told me to do an elimination diet.
While I had some digestion issues (high fructose foods, probably fructose malabsorption from my small intestine being wrecked) my main problem was sinus headaches. There seems to be an association between chronic sinusitis and celiac, but no studies backing that up. [1]
At the end of the day I've cut out gluten, sugar, caffeine, msg, and sodium nitrites as triggers to my sinus headaches. I went back and forth on a lot of these so I am quite sure of the relationship. I really did love bread, sugar, and caffeine and went back to them more than a few times.
The best I can describe the symptoms related to the sinus stuff is a withdrawal. For example, I feel OK when eating sugar regularly, maybe a medium bad headache here or there, but when I stop fully I get a horrible one, sometimes accompanied by throwing up, cold sweats, shaking, etc.
There is some research into opioid like effects of gluten. [2] I originally came across the concept on some fringe science about the bodies of people with autism treating gluten as an opioid (and advocating a gf diet for them). It resonated with me because the symptoms I experience are very much like a withdrawal. It's hard to talk about though because there isn't research backing it up.
If any medical students are reading this and want to study it, it's a pretty undiscovered field.
1. http://www.aaaai.org/ask-the-expert/coeliac-disease-sinusiti...