Ok so if she was already sensitive to noise, does she have any other little quirks like being sensitive to smells?
Has the Teacher raised any concerns so far? Is she settling in well and getting on socially? How does she do on this simple progress checker?
It might be worth asking to see the Teacher and talking about the problems you’re having at home and checking everything is ok at School. There is always the School Nurse service available for advice on things like this as well 
On a practical level, and to help you get more sleep, could you try her with a mattress on your bedroom floor?
Often a weighted blanket can help too as the weight gives them physical reassurance.
Introducing some form of meditation might help as well. There should be guided meditations aimed at this age on YouTube.
Does she have any sleep associations like a light show, a favourite teddy or a Yoto player?
It might also be helpful to try an earlier bedtime. This may seem counterintuitive but she could be overtired, and I imagine you are at the moment too.
Getting out in nature this weekend might help her to de-stress, maybe a walk in the woods or by a lake or canal? Walking by water is proven to have a very beneficial affect on stress and anxiety, have a read up on Blue Health.
Sorry this has turned into a bit of an epic. I hope you find some of it useful and sleep returns soon for you all 