Dizziness occurs in 1 to 2 out of 10 people who have whiplash injuries.  As with any CNS symptom, you need to tell your doctor about this problem.  99% of the time, this is not caused by anything serious.  It seems to be caused by many factors, but the most common are:

There are other, more rare, but also more serious things that can lead to this problem, so again, consult your doctor if you have any questions.

Caution!  Many patients get operated by surgeons looking for "fistulas".   This is a break in the canal in the inner ear presumably caused by the whiplash injury.  This is rare.  While it should be treated if present, any recommendation for such a surgery should be confirmed by a second opinion with another ENT specialist.  In my experience, very few patients have this problem, while many patients with chronic dizziness from a car accident  are operated.