OP, this is such a difficult situation. My youngest son began 'school refusal' in Y7. It seemed to come out of the blue to us. He was always, in our opinion, the stable child. Our eldest was the one with the 'problems' (autism, MH difficulties).
We worked with the head of year, the school social worker (I forget the correct title), and a very helpful head of safeguarding. Eventually, he began to attend and, at that time, it seemed like there was some bullying going on.
Then, after a period of calm at school (he was terribly disturbed at home), our youngest began full scale 'refusal' in Y9. I tried 'old school' methods of dragging him out from under his bed, bundling him into the car and getting him to school, only to have him rush back in the car, lock the doors and refuse to come out.
Those types of approaches were damaging to him in the long term, but I had to try everything. He was diagnosed with generalised anxiety disorder and received CBT from CAMHS. CAMHS stopped the treatment because 'he wouldn't engage'. We received tuition from the local authority for five hours a week, in English and Maths. He hid from the tutor for seventy percent of the time.
I could go on, but to summarise, we had an extremely disturbed young man on our hands. I took time off sick, and eventually I was able to work from home.
At home, he needed the environment to be rigidly controlled and predictable. Over the years this got worse. His older brother left to go into residential care, so it was just me and my youngest.
In retrospect, I wish I had stopped when he first started to refuse school and insisted there was some sort of assessment. He coped at primary school because he could camouflage and mask. He could not do this as well at secondary school, and there was some bullying due to his vulnerability. He never really coped.
It is obvious now that he is autistic (like his brother and father) and that his sensory issues, co-occurring anxiety and communication style (he talks incessantly about cars, for example) have been barriers to him making friends and coping. He has, in my opinion, PDA, but since he has refused to engage with services, nothing, apart from the anxiety has been diagnosed.
This has been a long description of my own situation, but I would really advise you to get to the GP. Try to start the assessment process. There is something behind the anxiety and the sensory issues your daughter is experiencing, and this is not likely to go away.
In my experience (and this is only my experience), the school were limited in their approach and the wider LA were seriously lacking in their response to a child essentially going without meaningful education for years. My son is 22 now and has serious mental health problems and the same need to control.
This behaviour and pressure does break you, but your daughter is young enough for you to insist on a more thorough assessment and a more proactive approach to finding what is causing her issues, and how she can be helped.
Apologies for the very long response.