Sometimes symptoms of whiplash last long after an accident. In these cases, a person may be said to have a "whiplash-associated disorder" (WAD). This might require medical attention.
A recent study found that the movement you describe (moving the head toward the chest and back) is typically the most difficult for people with WADs. The ability to look left and right and tip the head to both shoulders is also reduced, though not as much.
A doctor and/or physical therapist can help you deal with the painful effects of whiplash. Talk to your doctor about treatment options. There are exercises you can do to make neck movement more comfortable over time.