FYI, you can often get knots or
trigger points in this area. When you next feel it, have someone press hard on the area with their
thumb, if it increases the pain, then its a trigger point/muscle knot. Heat or ice are good remedies, then appropriate stretching etc. If you are riding hard on a bike, the body position alone is probably aggravating things.
That said, if you are a woman, then it potentially can be a sign of chest pain felt atypically.