Hi, Argamemnon. Breathing difficulties and shortness of breath are not the first symptoms that come to mind when you look at symptoms of celiac disease; if that's your problem, you're much more likely to have digestive system problems like gas, abdominal pain and distention, and constipation or diarrhea:
Celiac Disease
Breathing difficulties and shortness of breath suggest to me conditions like emphysema, bronchitis, or congestive heart failure. Rather than try to diagnose and treat yourself, and perhaps allow your condition to worsen, I would see a doctor right away, describe your symptoms and see what they suggest. HTH.