I've done the Allatess test, but I'm not sure how accurate it was. On the bright side, I did discover some new foods that I liked, as I needed to eat something new to replace the old stuff I was avoiding.
A food elimination and challenge diet would take awhile and be tedious with tracking, but I think it would give the most accurate info. Starting with the most common allergens like wheat, corn, soy, eggs, dairy, peanuts. Eliminating them one at a time. See how if you feel better if you avoid the food, or worse when you add it back.