The problem with "trying" the gluten-free diet to see if it fixes whatever ails you is that you may find -- as I did, as so many others do -- that once you are off of wheat, rye, and barley, you may not be able to eat enough of the stuff ever again to get an accurate diagnosis. This phenomenon is well-known to knowledgeable gastroenterologists who deal with celiac disease often: for many people, the less gluten they eat, the less they tolerate it.
There is something called a "masking effect" that makes it so that you have none of the obvious symptoms while eating those toxic grains, but once you begin to remove them from your diet, you become sensitized to them and find you experience some nasty effects (diarrhea, nausea, constipation, malaise, brain fogs, and so on) which will make it so that you will not want to eat enough wheat bread to get tested. (A milder version of "masking" is familiar to most of us who know someone who started smoking: at first the new smoker coughs, perhaps gags, and gets dizzy, but constant, persistent exposure to smoking makes these signs that the stuff is not good for you go away. )