Zoo, I'm sure at times DH would think I was a bit like your DP. I take antidepressants for DS1's sake. He is better when I am more level. His emotions are closely aligned with mine. If I am down, stressed etc his anxiety is higher. DH copes, sleeps etc. much better than me, but I put on a mask and pretend because DS' and DD2 need me and I am determined to give them a normal a life as possible as DD1 would want.
Anne and Katalex, at a very basic level you can have cards - red not OK, amber anxiety rising help me not get to red, green OK. Doesn't require speech, but does require an ability to know how one is feeling - something we are working on. Anne, written communication can be so much easier for high functioning teen girls.
An ASD diagnosis will bring your DD understanding of herself. It may bring understanding from others, at least in some people. School could ask the ASD specialist teacher for advice. It will bring her future protection in adult life under the Equality Act. It will bring with it an ability to apply for autism support via DSA for university. There may also be local autism support groups or services, or after care. Although you don't need a diagnosis for DLA, an assessment is evidence of need, and you do need evidence. At a more general level an ASD diagnosis allows you to name an ASD specialist school - something we can't for DS1 because he doesn't have ASD (though does have complex MH problems, and a diagnosis of something that has some similarities to autism), despite the schools potentially being suitable.
The GP can chase CAMHS, can test for deficiencies - particularly B12 and VitD, may know of local charities that they can direct you to.
If DD really can not manage school, then you need to get her signed off, the LA will become responsible for providing education, and apply for an EHCP. And via that or otherwise your DD would benefit from seeing an Educational Psychologist, an OT and SaLT.
You need to get to the bottom of why she's not going to some classes. What's different? Teaching style, her confidence, the environment, the work is too difficult (objectively rather than DD just saying that) etc. Why can she not go to theory music lessons? Why does the fact the English work is unrelated mean she is struggling? Without knowing why she's struggling you won't be able to move forward.
Look up parental leave.
Hospital appointment this morning didn't go well, the break needs resetting under GA, but they haven't got a suitable bed to admit him to at the moment. The staff were brilliant with DS though.