Get a Lawyer!
Do not accept ANY LOSS from this including Associated costs.
Make sure you get a brand NEW CAR
They must pay the full cost of a rental.
DO NOT SIGN ANY RELEASE until all is agreed and paid as agreed.
I would go to the doctor and make sure you are ok. Dont just assume it. Often problems take time to show up and they can be serious and expensive.
And remember your insurance premiums may go up. Get a settlement from them.
The insurance company is NOT your friend no matter how nice they may seem.
I have been through this and have been the "reasonable" party to my ultimate detriment. Never again. This is like business it demands a hard nosed approach so that you do not get taken.