Getting an assessment may take some time. There is some useful information here:-
https://www.autism.org.uk/ (if indeed it is autism). I do not know if it autism, but there is a good starting point.
If it is autism, one of the issues is a high level of sensory requirement and these children are massively energetic (I had 8 years' experience as a step mum to an amazing lad on the spectrum who has now grown into a wonderful young man and of whom I am immensely proud).
Something that helped enormously to calm was a weighted blanket. (There are other weighted products available, like lap pads etc). There are loads available online. Until something formal is in place I would recommend something like that. Also structure and routine is very important (as mum is probably aware). Discipline is very difficult because very often sanctions and punishments are of no consequence on the basis that there is a different thought process. My stepson took things extremely literally. I remember one day hissing I'd had enough and was going to run away with the gypsies. Then I had to field 20 questions about who were the gypsies, where were they, how long would I be gone and what were their names and would I be back to cook pizza for dinner.