Thanks for writing to us.
A pain which is in mid chest and comes always on exertion and relieves by rest is likely to be anginal or cardiac or heart pain. But if the pain comes suddenly, comes as a sudden very sharp pain
, lasts for less than a minute, can be elicited by touch or pressure, does not comes up on exercise/running/exertion, it is more likely to be non-cardiac (non-anginal).
Since your pain is associated with exertion (even though it has some atypical features) i would advise you to see your cardiologist and sort out the issue.
feel free to discuss further.