Residual pain and loss of motion from cervical spine (neck) injuries associated with car accidents are often called whiplash disorders. You didn't mention how long ago the accident occurred. If it's been more than three months, your condition may be considered a chronic whiplash disorder (CWD).
Whiplash disorders or CWD are often accompanied by significant muscle guarding and splinting. The muscles around the neck contract to hold and protect against motion that could cause pain. Sometimes changing this movement pattern can cause an initial increase in pain such as you are having.
Neck range of motion (ROM) may be a better measure of treatment success than pain relief -- although pain relief is still an important treatment goal. Relying on only one neck motion can be misleading because there is a greater chance of test/retest error in measuring motion. Using a combination of all six neck motions is a more accurate gauge of success.
Let your therapist know of your concerns and questions. Ask about goals and measures of success to help you better understand your treatment process and progress.