Most school screening are just that - very basic 5min tests often NOT performed by a lisensed Aud. Audiologist (rather a volunteer parent, or a school/division/district hoh/deaf co-ordinator etc).
These tests are almost useless ... They're done in an open room, with headphone and a portable testing machine where they test a few tones per ear and call it a day. The reason they aren't often able to give results is they aren't actually legally allowed to because the test wasn't performed by an actual AuD. (so they aren't actually allow to give any numbers etc, because their often very wrong).
I'm competely deaf on my right side +120db loss ... And I was able to "pass" the school hearing tests for years .... I just watched when they pressed their button and then raised my hand
Really, it's very very important that you push to have him properly evaluated by a proper AuD. (Audiologist with a doctorate or more in audiology). Keep signing with him, and perhaps consider taking some additional classes because it can do not harm whatso ever, but can be a great help.
Also, make sure when you talk to him that you face him, do call from other rooms etc, or turn your back when you talk.
Once he goes for a prper audiogram, demand a copy of the results (you have a right to them!) So that you can see exactly what is going on (we can help you read them)
HTH