From what I know and I have done tons of research on Celiac Disease and have a book from it. There is a complete difference from a wheat allergy and celiac disease.
It is odd though that he tested positive to all the grains containing gluten though. I know that if you have celiac disease, you will not test positive on allergy test because it is actually an intolerance. It involves your intestines v/s your immune system.
People that have celiac disease, they will actually show flattened villi from the biopsy taken during an endoscopy.
If it were me though and he tested positive to all of those things, I think it would be worth checking into, BUT................ In order to get accurate results, he would have to ingest gluten (wheat,barley, etc.) and you DON'T want to do that.
So if it was me, You know he is allergic to wheat, oats, barley and proabably rye. You are avoiding them, so you are avoiding all gluten. I would not worry rather it is celiac or wheat allergy right now.
If for some reason though in 3/4 years he start to handle wheat and oats again. He is eating them without many problems, I would then do a scope with biopsy's to see if it is Celiac. I only say that because so many children go undignosed for years and it can actually be masked and something later in life can trigger it causing a variety of symptoms and then they will try to diagnose him with everything else.
So, I would avoid ALL now, Don't do the scope or blood work now because you want get accurate/correct results. If 4 years from now he is eating wheat with no obvious problems, I would consider it then.
Hugs, Wendy