A rear-end is pretty straight forward who to blame.
Those neck injuries have a way of not fully coming to the surface for weeks or longer; you need to see a chiropractor, as an insurance claim.
It is a hard thing to let go of a car, you won't get a whole lot for an old one; but what you will get for pain and suffering if you are hurt will make the car's value look like small potatos.

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300CD '80 (now gone but not forgotten...)