I am not a doctor, but I'll try and help anyhow. I have experienced a similar feeling, though it generally covers most of my sternum, not just the top.
After I run for longer than I normally do (10 miles or so is about the threshold) or if I'm breathing extraordinarily hard. Some common examples other than at the end of a long run are after running the 1600m or 3200m race, both of which require some crazy breathing, or after a session of playing my Baritone Horn. After talking to a physician, I found that it is because I have a relatively narrow torso and I naturally have a lower lung capacity because of this. When you breathe, your ribs expand outwards to accommodate the expansion of the lungs. To do this, the joints where your ribs meet your sternum flex slightly. Because I've developed my lungs quite a bit with all my running and low-brass-instrument playing, my joints flex slightly more than normal. It's not life threatening, but it isn't normal. Generally your joints there don't flex as much as mine do, and it screws with some muscles in the area. Because of the tasks that I do that cause this, my heart is generally beating quickly and I'm breathing heavily, so that's another parallel with you.
Again, I'm not a doctor. This is just a story of a man who also has an occasionally stiff and sore feeling sternum at times after exercising.