Hello Good Evening,
As per your description you got car accident, so you got generalized injury including head and chest.
As you throbbing pain
in head, so you should go for a CT Scan
head to rule out ant hemorrhage or diffuse axonal injury
For chest Injury
, you should go through a Chest X-ray to rule out any rib fracture
Most probably it can be a inter-costal muscles injury which will take time to recover.
Overall you had not acute injury, so they did nor perform more test, but if you have some chronic symptoms then you should go through CT scan Head and X-ray Chest, to rule out any other significant injury.
Dr. Naresh Jain.