13 year old daughter destructive obsession with appearance

Hi. I am new to the forum but hoping that someone can offer some ideas/support.

My daughter is in mainstream school but her mental health has hit rock bottom and she can't see the point in life. She is on a part time timetable at school but is struggling to go in as she can't handle anyone looking at her as she feels too ugly, too fat, hair is too greasy. When she does attend a lesson she spends it focussed on hiding her face as she doesn't want anyone to look at her. She says that the only time she feels OK is when she has had a shower and is sitting in her dressing gown on her own in her bedroom listening to music.

She is obsessed with calories and asked that we put any treat food in a locked cupboard, which we have done. We also use the DLA to fund private weekly counselling. We are on a waiting list for CAMHS to discuss medication but there is an 8 month wait. I still have to sleep with her every evening and we have very sad and distressing conversations before we fall asleep. It's exhausting!

The biggest challenge really is school - I wish we could fast forward to college as she wants to study beauty and I am confident that once she is studying her passion that she will find it easier to attend, but if we can't increase her school attendance then I am concerned that college won't even be an option. I work full time and so home schooling is not an option - although that would be her preference. I am also not sure if home schooling would  be the right thing.

Is there anyone else out there in a similar situation?