My daughter was diagnosed Celiac too, her symptoms improved with gluten free diet (she had severe reflux, constipation, diarrhea, bloating, stomachaches, etc) but it was not enough until I went dairy free, sugar free, starches free and basically I eliminated all processed food. I found this "paleo" diet that saved our lives (I had the same problem) and I...
As far as I know Celiac is just one part of gluten sensibility, not all gluten sensibility people are Celiac, but any gluten sensibility is as bad as Celiac. I'd avoid gluten.