What would causes a mild burning sensation at tops of breasts and upper chest? doc says heart is fine.

Many things could: It could be pms or premenopausal/menopausal considerations depending on age. It could be reflux, allergic reaction to something like medication, or none of the above. A good workup may include some labs, keeping a diary of when these events occur and timing, pictures of the area to see if redness accompanies with heat or not. Suggest you get more info and return to your doc if this persists.