If anyone is moved by the OP's posts and replies from others in similar situations, please consider writing to your MP about the delays and lack of early intervention and parenting support with SEND in children. We have all seen the headlines about how funding requests have spiralled but leaving families until they are at absolute crisis point is making this worse, not better.
There are threads similar to this every couple of weeks on here now. I've been here for years and these posts do come up but I have never ever seen it so frequent. And it's horrific to think that joining an NHS waiting list for support means waiting further years.
Behaviour like this is the result of dysregulation which has compounded and compounded on itself. If OP had had access to the proper assessments, advice and support for her DD a year or two ago when concerns started to get raised, things might not have got to this point. It's completely unacceptable and it's not OP failing her DD, it's the support systems which are hanging by a thread.
I know writing to MPs won't help OP immediately (and OP I apologise for using your thread to say this) but the system is so incredibly broken and it's no good for the children or parents caught up in it. Six years waiting list is an absolute joke, what are you meant to do?
I hope you get something to eat, and some sleep, and you can have a better day tomorrow and make those calls on Monday (I'm going to make a meeting with the SENCO Monday morning and look into the right to choose) - these are positive steps and will be more helpful than reading a load of posts debating whether she's bad or sad and what you might have done differently. You've done everything that a responsible parent would do, it's just the systems behind you aren't there backing you up.
Asking the GP for melatonin might also not be a bad idea. It can be prescribed in cases of medical need, a lot of neurodivergent children don't make it in the right quantities so genuinely can't sleep. But if she is constantly wound up that will also make it harder for her to sleep which then has a knock on effect on her mood/behaviour the next day etc etc. This won't be helping and it might be something you can get in a fairly short time.
Try the Robyn Gobbel book. I completely understand it seems absolutely laughable that a book could help, but if any book can help it's this one. It's the one thing which helped me before my son went onto medication, and I had read an entire library's worth previously, all of which were very interesting, but didn't usually make any actual difference day to day. This one I would lock myself in the bathroom and go back to the helpful pages and be able to actually diffuse the situation as a result.
And seek out other SEN parents who get it. The MN threads on the SEN parents section or other online support groups but ideally, IRL/locally even if you only communicate online because you can't get any space from the DC.