Head and neck injuries are common after car accidents, even minor ones. Many people develop what's called a whiplash-associated disorder (WAD). Your symptom may be caused by a WAD.
Movement of the head and neck uses information from three systems. The muscles in the head and neck send information to the brain about position, speed, and movement. The inner ear (vestibular system) keeps us upright without dizziness and falls. Data from the eyes (ocular system) is also an important part of staying upright and moving through space.
Even minor car accidents can cause a problem in one (or more) of these systems. Dizziness suggests a problem in the vestibular system. There are tests that can be done to find out for sure. You may want to make an appointment with your doctor for an exam. Often treatment for this kind of problem is very quick and easy.