It may not be "Autism" but the thing he needs help with is: Yes he is anxious about school, I take him in every day before work as he said a boy was picking on him on the bus, and after one incident, as he got out of the car I told him to be good and I noticed him wiping his eyes as he walked away. I stopped him and asked what was wrong and he started crying and said he was worried he was going to get into trouble again. He worries a lot about letting me down.
This is exactly the kind of thing that CAMHS should be helping with. Unfortunately their ability to help in different areas differs widely, so they may not actually be the best people to help, but either they or a paediatrician should be able to help, and strengthen your case that the school needs to put in accommodations to help him cope.
My DD often answers "I don't know" and if you ask her how she feels it is worse (and can lead to a meltdown), because she really struggles with the thinking needed to be able to understand her emotions nevermind other peoples, and can't always match up cause with effect. Eg. Why do people get annoyed when I talk over them as they are having a conversation? Or why did that girl cry when I said she was a bit fatter than last year? Or....
The crying when others are hurt is a big sign, that needs to be discussed with a trained professional.
When my DD first saw CAMHS both her and I had suspected ASD, but she didn't seem to "fit". In an interview with me consciously not "helping" her - it seemed to be a very obvious possibility. Still her teachers didn't think it fitted her, but as they filled in questionnaires, they increasingly recognised the pattern. And I was fortunate the class teacher's could see the pattern, I know friends had real issues with the class teacher for their son, who couldn't, even though on the surface he seems more "obvious" than my daughter.
But it may not be ASD for your son, but just "social anxiety" is a real issue and professional help and support, will help you argue for the support and help your son needs at school. It will also help stop him being inappropriately punished.