If it’s a non fault accident, the other parties insurance will be liable for any hire car costs until your car is repaired (lets hope it is repairable)
I have read elsewhere, that some cars that would have been written off are now being repaired instead.
Whilst my Audi Q3 was in for repair after a non fault accident a couple of years ago, I was provided with a Jaguar F Pace and didn’t want mine back. So don’t accept a rubbish hire car.
Glad you’re ok ? and good luck.