Food allergy/FPIES

So my 7 month old has some sort of allergy/intolerance. I think it's to oats but anytime he eats oatmeal or those puffs cereals he vomits profusely and the dry heaves for like two hours. In between he is dead tired and falls asleep. It's horrible and I feel so hopeless. He also doesn't really like purees and I've tried BLW but that isn't working well either. We just moved so I'm working on finding a new pediatrician and hoping to get referred to an allergist but I was wondering if anyone had a kid with an issue like this?