My son has multiple severe food allergies. Our gastroenterologist and pediatrician would were the ones that recommended allergy testing for him. It sounds like your situation isn't quite the same on that front. However, we also didn't start the allergy testing process until he was turning 2 years old. Maybe it is age that makes a difference?
Allergy testing is not a waste of time or money at all. For us, it was a lifesaver (literally) and insurance covered a majority of the testing. It turns out that some of the symptoms that my son was having, and that we were writing off as related to other things, were actually anaphylaxis reactions. He just doesn't turn blue and stop breathing when he is having an anaphylaxis reaction (lucky for us).
Our gastroenterologist is Dr. Osuntokun. Our allergist is Dr. Vankatesh. Our pediatrician is Dr. Farias. I recommend all of them highly.