Imaging studies don't always show the cause of problems that last long after an injury. In the case of whiplash, chronic problems from bony or soft tissue injuries are called whiplash-associated disorders (WAD).
Chronic muscle pain, neck pain, headaches, and vision changes have all been reported after a whiplash injury. Weakness, stiffness, numbness, and loss of memory have also been found with WAD. Imaging studies often look perfectly normal.
Check with your doctor before going through the time and expense of a CT scan. A physical exam may reveal just as much information as imaging studies currently available.