Polyps can be found with x-rays. It's the only way to really see some of them. Doctors were weird with me when I was a minor too. They said they saw polyps but tried to give me allergy shots. I discovered the polyps when I sneezed one out.
There must be pediatric ENT's. I think you just have to look around, ask if they specialize in kids. Some do. Kids with these problemes are miserable, with ear trouble and other things.
My adenoids were big and my tonsils are really big. My ears are always plugged up from them. My throat swells like crazy, the whole thing, and my whole nose too. It feels like my nose is completely packed with cotton during allergy attacks.
I didn't understand your PITA thing, but after reading it, I think it's a good idea.