Rear ended at around 10mph 2 days ago and my neck hurts. the urgent care doctor the day of said i didnt need an xray. are the chances of fractue low?

Fracture?: I agree that chances of a big fracture is low. However, if your neck pain doesn't improve over time, then getting a study wouldn't hurt to rule out a small chip fracture. You can have a muscle sprain, but that should improve as time passes.

Whiplash Injury: Yes the chances of fracture are low.But your pain may be related to whiplash injury and if the pain persists,you should follow up with your doctor

Neck injury: As a trauma surgeon I see this daily. My recommendation is to get an evaluation which includes a CT scan if you have neck pain. You may have a negative CT scan - showing no injuries despite having neck pain. If the CT scan is negative and you still have neck pain then the next thing to consider is a possible ligamentous injury and an evaluation by an MRI.

Low chance: At this rate of speed and in a car with a proper headrest, the chance of fracture to your neck is very low. Most likely this would result in some pain for a short period of time. This could be diagnosed as a strain/sprain. If pain persists, then an evaluation is recommended.