Go here and watch the video.
The Celiac Diva explains some other food intolerances you can have, the whys, and the tests to figure it out.
I haven't done the test for this, but I believe I've got leaky gut syndrome like she did.
This video explains leaky gut syndrome a little better and the problems it can cause if left untreated (mine caused fibromyalgia, so you really want to look into this if you think it's a possibility).
What about you? Do you think you have additional food intolerances? Are you still feeling sick even though you're eating gluten free?