S.S.
My sister has celiac disease, which is mainly gluten intolerance which causes problems in your intestines. But since finding out, she has gone gluten-free and noticed many improvements in her health - skin, hair, mysterious aches and pains, anxiety, ADD - all much better.
However, food intolerances are totally different from food "allergies", which involve your immune system overreacting to something it perceives to be dangerous. I'm not an expert so I don't know how to describe it for sure, but the way I understand it is if you are intolerant to a food, your body can't digest it, and this can have a variety of effects.
I'm not sure if you can be tested for food intolerances in general (I think it is usually a process of eliminating things from your diet and re-introducing them), but there is a specific test for celiac disease that doctors can do. My sister was doctoring for 6 months before she happened to see a doctor who knew about the test, ordered it, and voila! They had an answer.