Its a well documented fact that in many cases whiplash can take a number of days, occasionally even weeks, to materialise, so don't for one second thing you're too late to claim for that, or even that it won't appear.
What I would suggest is that you substatiate it by getting yourself to the docs pdq, getting a sick note and a neck brace on.
On the car note, I would get it thorughly looked over, don't just assume bumber and exhaust are all that is busted - have a full suspension geometry check and adjustment done, and add that to the claim. Did you have your hand brake on when it happened? I (successfully) claimed for 2 flat flat-spotted Yoko's when I got shunted.
At the end of the day, there are professionals out there milking insurance companies for ridculous sums of money every day, and that is part of the reason that everyone pays astronomical insurance. I fully support anyone wishing to claim 'that little bit extra' for inconvinience and to stick it to the insurance company every once in a while, as you are just ensuring that you are not out of pocket and are fully recompensed for the inconvenience.
Good luck buddy