Does running correlate to jaw pain?

It can. I have been a runner for years, and there are instances where clenching during running can occur. Also, the jarring of running on cement, can affect posture and other movements, creating an imbalance. Also, many runners these days cross train. Other activities, like lifting weights can cause you to clench, causing jaw pain. You might want to consider a custom mouthpiece for your activities.
Possibly see below. By running you are increasing your circulation, obviously. This can then manifest and or magnify a potential dental problem in the jaw, like an abcess. You should see your dentist and get the area in question x-rayed.
Not normally. Jaw pain when running could be caused by a couple of things. Usually it is a tooth problem, either a large cavity or problem with the pulp or nerve of a tooth. Another cause could be ischemic heart disease or other cardiovascular issue. You may want to see a dentist to rule out any dental problems and get a physical with your doctor.
Possible. Possible. Due to jaw joint pain from clenching or jarring while running, rare ischemic heart disease can refer pain to jaw while running. Best to see an oral surgeon to help sort out jaw pain.

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