Hey Ruff, I am also celiac, and cannot tolerate wheat products or gluten, and have the same allergic reaction that you do. I was undiagnosed for many years and suffered a lot of damage to the villi in my bowel. This is the reason I have had problems with absorption of nutrients in the past.
Contrary to what many alkalising promoters say, its only when I increased my stomach acid, started taking bitters before every meal , and before bed, that my digestion, hydration, and absorption of nutrients became better. Probiotics, mineral and herb supplements have also helped a great deal. I also take Iodine supplements for thyroid, breast and reproductive organ health.
I always thought of my symptoms as being more like exhaustion, and that my body was literally starving for nutrients. It was actually the lack of acids and the lack of good gut flora that was killing me, rather than being acidic. Once this lack of stomach acid and gut flora, were sorted, my immune system has been fantastic, in fact my health overall has been great.