“Should I see a dentist or oral surgeon for jaw pain?”

I think you should see your general dentist first... if they have concerns they can refer you to an oral surgeon for evaluation...

Oral surgeon for sure

Depends on the location of pain, the severity, any associated oral or facial/neck swelling. Many sources dental pain can be readily managed by a conscientious and well trained DDS. One can always start with an Oral Surgeon, but may be advised at that visit the best course of action for that individual would be a visit to a general dentist. If the pain is severe, or associated with any oral or facial/neck swelling you should consider a visit with an Oral and Maxillofacial Surgeon first. Don't be mislead by corporate dentistry or by those general dentists who can "do it all." An Oral and Maxillofacial Surgeon has been specifically trained to manage the more severe matters.
Good luck.