Is he a quiet get on with it type?
Because ds broke his arm playing football aged 15yo in PE. He came out, and I spotted from across the car park that I knew immediately it was broken.
By 9:30 the next morning I'd had two phone calls from teachers, both horrified, but also surprised in equal measures. They said they'd done all the normal tests for broken arms and he'd been fine with them all. He'd told them it didn't really hurt and he finished the football match (playing goalie). And he'd done the last two lessons of school, and said he didn't need to go to medical.
I told them that. Firstly ds will avoid medical attention if he can get away with it. Secondly he has a high pain threshold (with appendicitis his pain out of 10 varied between 2 and 4, and he was nearly sent home again) and thirdly he wouldn't want to miss any football so wouldn't want to stop and he will deny any injuries in front of others.
I am totally confident that the teachers did all they could and it was not their fault at all.
And apparently it was a very good save too.... that's the main thing he cared about.
He would actively go out of his way to prevent a teacher (or anyone) realising (as dd1 would. Dd2 would be more likely to be at medical and suggesting she was better at home for a paper cut...) So it can be hard for a teacher to know.
You can say the teachers knew he wasn't writing. But was it in a "I'm in far too much pain to write" or a "quietly doing anything except getting on with work" because that's what ds does more often than when he's broken his arm!
And there's an aspect of knowing the child. The PE teachers then knew that if they were in any doubt with ds he needed to be checked out - even so he managed to hide from them a gash from a stud a few weeks after he was able to play again. (according to him it didn't need cleaning as it was "clean mud"), but he was quite disgusted to be sent for a check up another time when he said "it hardly touched me". They wouldn't have sent him to be checked if they hadn't been aware of this.
It's also from seeing it in ds, he did get worse. So what initially looked like a brief "ouch", then started swelling and he would have found convincing the teacher later that it wasn't a problem a lot harder.
What I suggest you do, rather than getting stressed is start off by factually informing them that his arm was broken at school.
See their reaction.
If they brush it off, then ask to meet with the teacher and find out what happened from their point of view.
Accidents happen, things are missed by parents as well as teachers. A positive relationship between you and the teacher looking at how to move forward so such a thing isn't missed another time is a good thing.
Sometimes lessons do need to be learnt, but going in with a "work it out together" attitude is far more likely to get the right lessons learnt than going in aggressively.