Where I live it's a 4 year wait for diagnosis. Then you get the diagnosis and just discharge no support. I would insist the GP make the referral but go private if you can afford
Raise it with school. If she's better supported at school it will help at home. Look up coke bottle effect.
The controlling makes me think of PDA. Look that up and see if it resonates. PDA society have a lot of info on their website.
I also think when considering neurodiverse people it's important to have a basic understanding of sensory processing difficulties which are a common comorbidity and if you are dealing with that it's the fastest way to improve behaviour by helping her with the SPD.
I agree with you social services won't be any help. A disability social worker are different and nice but to get one you need a child so affected by their disability they can't go to school or access social life etc so trying for one will just land you with a safeguarding assessment.
Possibly consider if school is too challenging an environment. Join some send groups and ask advice. School should be supporting and making accommodations regardless of diagnosis (but often they lie say can't help without diagnosis. This is why you need other send parents advice it's a massive massive battle for basic help).
I have two autistic kids. One diagnosed one not yet. Ultimately no matter what support I want or fight for the best help is educate yourself on your child's needs and sensory profile. It's what I've done that has helped my kids the most.
I'm not sure I can help with that feeling if being abused by your own child. I have a lot of resentment for what my child's needs have done to the family my work and the effect on his siblings. I live in fear of him getting stronger as he grows up. One thing I always say is try to think about how the child is feeling to act like that. It's bad for you definitely but they are living in those feelings.
Oh and lastly try to work out the triggers for the behaviour. This is why I suggested look into SPD it may be she's too hot or there is a buzzing light or itchy collar etc etc but it may be something unpredictable has happened and triggered the anxiety that is the root of the violence. Personally I set up my iPad to film constantly and every hour if there had been no incident deleted and started again. Then I spent my evenings watching it back to work out what set him off each time. I then adapted to avoid triggers and things have improved for sure