Appearing to be fine at school and exploding at home signifies there are unmet needs at school. If school was easier, home life would improve too. The school needs to be providing more support. You could ask if they run sensory circuits, nurture group &/or Lego therapy. Do they have anyone who can support emotional literacy/Zones of Regulation work? Are they breaking instructions do, giving them in written form, checking DD has processed instructions? Has DD tried using a laptop or tablet to record work rather than writing?
Does DD use noise cancelling headphones or ear defenders? If not, it is worth trying them. Also, thinking about things like placement within the classroom, proper movement breaks, somewhere quieter to eat at lunchtime, arriving/leaving 5/10mins early or late through a quieter entrance.
For the sensory overwhelm, has DD had a sensory OT assessment? Some people find the book the Out of Sync Child helpful.
From your posts, I suspect DD would be eligible for DLA. Have a look at the Cerebra guide. I suspect you are doing things you don’t realise count.
You could also request an EHCNA. You may have to appeal, but you can get EHCPs for DC who mask &/or are academically able.