Your car impact was violent. After the initial trauma and confusion, you inventory yourself for pain or injury, and if you are lucky you feel or see none. However, you should still seek medical treatment. Delayed symptoms of injuries are extremely common after traffic collisions. Often this delay can be more than 72 hours after the collision. These injuries may worsen by engaging in everyday activities and cause more damage and a longer recovery. By seeking immediate medical treatment these injuries can be properly diagnosed and treated in a timely manner to avoid permanent injury. There is an abundance of literature describing delayed onset of symptoms because they are so common, insidious and important (1)

These delayed symptoms may indicate a significant injury. You may have been taken to the emergency room following a motor vehicle accident where X-rays were taken and an exam was performed. Most times the X-rays do not show any fractures or significant pathology. The emergency room likely diagnosed a Sprain/Strain and you are released with pain medication and muscle relaxer medication. The emergency room is designed to treat emergencies. Once they have established that you are not in a critical or intensive state, you are released. By no means does that mean you are well, or have no significant injury. It is important to follow up with a doctor that focuses on treating motor vehicle accident injuries. This way you can be assured that any injuries requiring treatment will be diagnosed and properly rehabilitated
References

1 – A Distinct Pattern of Myofascial Findings in Patients After Whiplash Injury
Archives of Physical Medicine and Rehabilitation
Volume 89, Issue 7, July 2008, p 1290-1293