You might be allergic to gluten, which is not quite the same as gluten intolerance but unpleasant nonetheless. The reason I would tend to suspect allergy over intolerance is the immediacy of your symptoms, though it is possible you're very intolerant and sensitive to it. I am only mildly gluten intolerant and only get symptoms after eating a certain quantity of it over time, but I've heard others report pretty immediate reactions.

Have you tried avoiding all gluten for a few weeks to see if you feel better?