Talk to your own insurance company. Give them info of other driver like insurance, name. Don't discuss coverage limits and other specifics to anyone else.
The other insurance company will contact you and ask for a statement. Just tell the truth, it will set you free.
Get a few estimates. Not sure how it works in your state, but in California we are allowed to choose whatever shop we want to.
Get car fixed. In the end, you still lose in other ways, even if it isn't your fault. I know, I've been walking for 5 weeks while my car is being repaired. Stupid uninsured motorists.