It seems that you are indeed suffering from cervicigenic headache (chronic unilateral pain that is referred to the head from either bony structures or soft tissues of the neck).
Two things are exclusive for this type of headache and help to distinguish them from migraine.
The first is that the headache can be made worse or actually onset by head or neck movement (you'll have changed neck posture or restricted neck range of motion).
The second is that there is marked tenderness in the suboccipital region or just under the base of the head.
History of car accident is also suggestive for this type of headache.
Medications alone are often ineffective or provide only modest benefit for this condition.
Anesthetic blockade, thermal neurolysis, combined with physical therapy is recommended, too.
A variety of surgical interventions can be suggested in certain cases.
Best wishes!