My SS masks his ASD, it took a long time to get anywhere near a diagnosis.
He is an angel at school and was at nursery too. Yet I would end up with bruises, scratches, a black eye, nose bleeds...totally beaten up by him. He hurt his baby brother, strangled him to the point that he was blue (my husband was in the toilet and I was packing my bag with my lunch for work and he was left alone for 1 minute). He would smash things and just scream, he also used to urinate on the living room wall on purpose.....but no, as far as they were concerned, no problems and no help.
I met him when he 14 months (he has been with my husband since birth and very little contact with his BM so I am the woman who raised him since then) and I knew the moment I met him he had ASD.
He is now 8 and FINALLY school got on board when he was about 5 and a half but still half heartedly and we have our final diagnosis appointment on 17th March, had the 1st part with the computer assessment which said ASD.
Thankfully he is very rarely violent anymore, 1 incident at home in the last year. He is able to control his anger much more now. However he suffers with severe anxiety and talks about wanting to be dead a fair bit but then getting terrified of certain things causing his death like fires ect.
You are doing nothing wrong, it is hard and just keep seeking help. Go to the GP and you can start the referral process, that is the way we had to do it. They referred us to a paediatrician and child psychologist and although the process has been slow the end is finally in sight.
However, a diagnosis doesn't really do much, but you an access different services and get more support depending on your area. Thankfully my area has a fair amount. We also want an EHCP plan in place for secondary school as I know he won't cope in mainstream.
Anyway, I am rambling, but you aren't alone. You are doing your best and love him. Keep trying to seek help and you will get there in the end!