Yes, a small accident can do damage. the energy is transferred into your body because you do move around, even with a seat belt. It isn't just movement in the area of your spine that got operated on, but any movement anywhere...it's all connected.
If you did not file a report with the police, I am not sure what your options are. Insurance gets really sticky. But, I agree with the other post that you do want to let your doctor know. Then they can watch for things that they might not be watching for with "normal" recovery.
Best of luck