She hasn't referred you to SS because she believes you're a shit parent at all , far from that I'm sure. You sound like a fantastic mum who recongises that things need to change for you all to live a better life.
My sister is severely autistic with associated learning difficulties and probably other undiagnosed stuff. Takes an antipsychotic and anti depressants. It got to the stage that my mum was put into hospital with concussion before she accepted the situation at home wasn't good. My sister was a little bit older , she was 19 or 20 (can't quite remember) so school was no longer an option unfortunately.
SS assessed the situation for a long time , did various referals to day respite, and weekend respite, local services for disabled adults etc but kept saying best option was for her to go into some form of residential care. As she was over 18 it wasn't social care exactly, but she was placed into a scheme run by a local well established charity. It's sort of like very sheltered housing. She shares a flat with an older girl who has downs syndrome, and downstairs there's 3 lads with various difficulties too. They have 24/7 staff on site, usually someone is in her flat from 7am until 10pm with phone access and door alarms overnight (so if they approach the front door an alarm rings).
They have stuff to do every day via SS referals and through the charity, and there are options to meet other people too in the community. Her wants and needs are respected and met. Her staff are able to help do her what she would like within safe limits.
Mum is very involved with regular reviews, phone calls, and visits - sister can home as and when she wants with staff and mum's agreement.
Sister also knows that unlike Mum's, her staff are in a position where they will take action against violence and she knows she cannot hit them or threaten them as she'd lose her place. They can also support her in keeping the rigid routine and relative stability she needs , so she's less likely to kick off.
SS were also able to identify needs that my mum had, and myself as the older sibling, and were able to help to some extent there.
Mum was petrified - both of allowing SS to help and of letting go , but it has had a hugely positive impact on everyones' lives so far. Sister has a life she couldn't have had at home at all , my mum couldn't care for her 24/7 and neither should she have to. I think she felt very guilty and like she'd failed but in reality failing my sister would have been keeping her at home I think, putting her into residential has given her the chance to thrive.
I know the issue is a little different as your son is younger so there would be other issues I imagine , and I know SS aren't always fantastic - but this might well prove very helpful for you all, I would see what sort of help they can offer. They aren't coming on the premise of you being a bad mum, you're the total opposite.
I hope this helps , even a little bit.