To answer your question -- yes -- a break in the chin bone or mandible is a very possible cause of your pain. That being said, there are other causes of chin pain that should be evaluated. I would recommend that you see your primary doctor
to have this evaluated.
A trauma to chin can cause damage to many different structures in the area. A possibility is trauma to the bone -- or a fracture
as you suggest. The mandible is actually a very strong bone -- so a complete break might be less likely. That being said a partial break or crack could have occurred. Talk to your doctor about this -- he or she can evaluate this with an x-ray.
There are other structures that could have been damaged. The soft tissue or muscles in the area can be damaged by the trauma. This results in inflammation and swelling which can take weeks to heal and improve. There can also be damage to the skin which can cause pain. Rarely, these openings in the skin can get infected -- known as cellulitis. This can cause worsening pain.
Talk to your doctor. Evaluating the cause of pain is important. After knowing what the cause of the pain is, your doctor can prescribe treatment for the pain. Good luck!