Better see a doctor, I got rear-ended in an old Mustang (no headrests) about 20 years ago and got whiplash which didn't start hurting for a few days.
First time ever seeing a real X-ray and it's my own neck and skull!
Doctor: See these vertebrae, they're all straight?
Me: Yes, is that good?
Doctor: NO, your neck is suppposed to be curved.
Still get a sore neck some times.
Also found broken parts all through the car, not just the tail light panel.