See a doctor. That is an interesting symptom. It could be heart disease if you are at risk for that. The heart can hurt anywhere and it comes on with exercise, goes away with rest. The jaw is more typical place for heart pain, but under the tongue is close. Otherwise something in the mouth itself is causing the pain when the circulation there is changed from the running. It is worth seeing your doctor.
Tongue pain. A pain under the tongue during exercise may indicate an area of venous congestion, possibly from either a venous dilation or if larger, a venous malformation. This type of vascular birthmark often swells with exercise or valsalva maneuver, and improves with relaxation and deep breathing. This is best examined by a ear, nose and throat physician to rule out any other disorder.