My personal experience is the entire medical community seems to have an avoidance issue WRT food allergies. Oh who knows some kids are just like that. Thats just how some kids are, why don't you wait and see if he catches up. I'm sure that's not the case. Well some kids just develop at a different rate mentally and physically than others. They'd rather MRI my son for suspected stomach cancer than test for allergy antibodies (or was it just xray? It was awhile ago). Seriously. They had us all in suspected cancer mode before they broke down and tried allergy testing.
Eventually, after much arguing, the pediatrician ordered a blood test, referred him to a gastroenterologist, who did some crazy stomach wall tissue biopsy after draining about a quart for innumerable blood tests, and finally, they're like "yeah, he's severely allergic to gluten per both biopsy and blood tests, so stop eating that". And casein and soy.
I found it remarkable how hard you have to push to get tests done for a diagnosis like that. I believe in for profit industry, follow the money. The worst medical scenario for the patient or the parents is probably cancer or something awful like that. The worst medical scenario for the doctors and adminstrators is an illness that is treated by a "simple" diet change and requires no expensive pills, no expensive followups, no expensive surgery, diagnosis wasn't too expensive other than the tissue biopsy work... that's why you have to fight fight fight to even get tested because that diagnosis is a nightmare scenario for the docs.
The point of all this is his development rate skyrocketed once we got him proper food, and he's pretty near caught up to his peers, which is cool. So you'll have to fight extremely hard to test for food allergies, but it might (or might not) pay off. (edited to add there may be other financial nightmare scenarios for doctors which are hard to get tested. Hmm, how about vision testing? Can't learn to read if you can't see the page, but if you can avoid getting the kid glasses you can milk that cow for money for a long time WRT special needs reading classes and such. My daughter had that problem.)