First, unless I missed something I didn't see anywhere that the OP said he/she had celiac, all I saw was “gluten sensitivity” which is not the same. In a video I saw a few months ago on Youtube, (and which unfortunately is no longer available) the difference between gluten intolerance, sensitivity and celiac was explained. If I remember correctly an intolerance is more of an allergic reaction and sensitivity is difficulty digesting it which can lead to full-blown celiac in some individuals.
Next, I disagree with the statement “wheat is wheat”, the GMO wheat we eat here in the USA has several extra sets of chromosomes and the gluten in it is not quite the same as natural wheat. Dr. Davis explalins this in his book “Wheat Belly” and in several videos available on Youtube as the reason why so many people are having trouble with wheat and he is of the opinion no one should eat it. Also, “gluten is gluten” is not entirely correct, all grains contain some type of gluten but only some are really bad for celiacs, also, each grain has a different proportion of gluten, and naturally, wheat has the highest percentage of all, whereas oats has the lowest, which probably explains why many people only seem to have a problem with wheat. The video also mentioned that all glutens appear to cause some intestinal inflammation though, but I imagine that is more of a problem on a heavily grain-based diet and is probably the reason why some, like Dr. Mercola, actually recommend a grain-free diet for better overall health.