Dizziness and vertigo are fairly common symptoms after an auto injury. There are a few different causes for these symptoms:
The most common cause of dizziness is injury to the tissues of the neck. When the ligaments and discs of the neck are injured, inflammation and scar tissue can affect the nerves of the spine that help us regulate balance. In fact, recent studies show that most patients suffer from balance problems after an auto accident, even if they don't have symptoms of dizziness.
In some cases, vertigo can be caused by direct or indirect brain injury.
Here are some important articles that explore the issue of dizziness and vertigo after an auto collision:
Postural Stability and Neck Trauma
More on Proprioception and Whiplash
Objective Evidence of Nerve and Muscle Changes after Whiplash Injury
Whiplash: The Neck and the Brain