Indy is correct..............don't fight this by yourself.  That's why you pay insurance premiums.  Call your agent and get your company involved and let them do the fighting.    And correct again.......don't sign a single thing till you are 100% satisfied with the deal.  The other driver's insurance company is likely going to try to low-ball you and intimidate you into settling for what they offer.   You're holding some cards in this game as well, don't buckle.

By the way, looks to me like you may have been pretty lucky to have avoided injury.   Had a chiropractor tell me a few years ago that the neck pain I was having was from a whiplash.  I said no, not me.  He asked me if I'd had a rear-end collision 15-17 years earlier.  Well, yes, as a matter of fact, I had.  His opinion was that many neck problems he saw in his office resulted from accidents that long ago and just now surfacing.  Take care of yourself, and be aware of any latent pain/injury.