A more efficient method is a skin allergy test (skin prick test). It allows for testing lots of allergens in parallel.
https://en.wikipedia.org/wiki/Skin_allergy_test
A quick search shows that it works for gluten intolerance/celiac disease too.
My mom went through this back in the 80s or so after having mysterious issues - turned out it was raw(ish) onion that was the culprit.