Its stressful isnt it, sorry youre having such a rough time.
Sounds similar to ds, seems with ds his sensory and no eye contact are very connected. He would say things were crawling on his skin and want to brush them off when people looked at him, similar to your ds.
I agree the lack of a garden and being able to run around might be affecting him, especially if he has sensory difficulties.
I would tell ds that even if people were looking at him, he didnt have to look back, which seemed to help a bit, he didnt feel so threatened. Maybe you could tell your ds, instead of shouting when people look, just dont look back?
You could also suggest to school, that maybe he needs to have someone quiet to go, when he gets to the point of wanting to shout at people and is feeling overwhelmed? So instead of shouting, he can have some quiet time?
There are some exercises you could do with him, if he isnt getting much to run around etc. see if that helps