Since it sounds like you've had no help, this might be of use (it's basic so won't be enough for severely affected people without a therapists support, but if you've so far tried nothing then it's worth a go). There's a book in a series called Overcoming, there's one for OCD. It's self-help CBT. What DD needs (and may need therapy to help achieve) is coping strategies for the thoughts that come from OCD. Relying on another person for reassurance isn't a helpful strategy, because as you've discovered, 5 seconds after you've reassured her the thought is back and she's wanting reassurance again. It's completely impractical and leaves her dependent on others the entire time. She needs to develop her own coping strategies that don't require other people's input to implement. CBT can help with that.
Honestly I'd forget education right now. IMO it's completely overrated. When she's 25 nobody will care one jot what qualifications she has. Most people with ASD aren't in work, that's fact, however much you may not like it. A few GCSEs won't make any difference either way.
What will make the difference is her mental health and ability to cope with the world. So education around that will be of far more use to her than time spent analysing shakespeare or learning Pythagoras theory.
She can educate herself from the library or YouTube for free, on all manner of subjects not just the national curriculum ones taught in schools. Let her learn about the genetics of Peruvian mountain goats or how to knit a jumper, if it calms her down. All learning is exercising the brain, it doesn't matter the subject. There are various websites run by charities where she can learn about autism. GCSEs are available to mature students at college, not only youngsters, although there'll be a fee once she's past 18, but if she's on benefits that fee will be minimal.
Trying to shove a square peg into a round hole isn't helpful IMO. Best thing she can do is focus on her mental health and learning to navigate the world as someone with ASD. When she reaches 18 if she's not capable of working she can claim UC and possibly PIP too. In her current state (if it's ongoing) she probably qualifies for DLA (the children's version of PIP) which she can then spend on anything at all, so a home tutor if that's what she wants and family budget is the only issue.
You need to be practical, there's very little chance she's going to be seen by CAMHS before she ages out of it so you'll be looking at a referral to adult MH CMHT when she's 18. It sucks, I know, but that's life. Banging your own head against a wall that won't yield is a waste of time and energy.
Hopefully she'll recover enough to work one day. If she does, she can get an entry level job that all the other people without qualifications can get. We're indoctrinated that GCSEs, A levels and university degrees are the only path to any kind of life at all. It simply isn't true and that mindset puts a lot of unnecessary pressure on someone who's health is already in the gutter. Pressure is the last thing she needs right now.
Many jobs/industries, if the person is capable, they can work their way up even if that means switching companies every few years. As an adult you're only as good as your last job, nobody cares what GCSEs you got (if any). If a person isn't capable of working their way up a career ladder, for either intelligence or health reasons, then no amount of GCSE certificates is going to get them a better paid job. So I'd forget school and focus on quality of life at the moment. You want a same and happy child, over and above a well educated one.