Hello Flummoxed, sometimes people with autism may also have OCD in some respects, although I'm not a doctor, but some obsessions and compulsions may overlap, such as continually washing her hands, however, if parents don't have OCD then it's so frustrating to try and understand why a person has to carry out these continual reactions because neither parent has it, then why should one of their children develop it, so you feel confused, exhausted and have no answers or any solutions on how she can stop it, especially when you have family/friends around, then how can you explain this to them, it isn't easy, but it's nobody's fault.
Some people can overcome this illness while others either need help to control it, lower its impact or learn how to hide it from other people seeing, but everyone is different.
I've been taking medication for OCD and depression for a long time and certainly, my doctor would not discontinue it, nor would I ever want to, but what it does is make me feel more stable, although I still have obsessions/compulsions but I hide everything I do so nobody else can see.
I realise this may not be the case for your daughter but a psychologist who deals with OCD will be able to help her and hopefully ease your concerns.
Please ask any questions you want an answer to.