Don't need anymore details. I have experienced the same and my guess is, it is fairly common to those just starting either this particular lift with heavier weight, or those who do flyes (regardless of how useless flyes are as an exercise).
The picture above is what your sternum looks like. Do you see the ribs? They are attached to the sternum by what is called "costal cartilage". It is a slightly elastic material attached to the end of the bones in that area. In other words, it can stretch a little (your long bones can also bend a little without breaking if you didn't know which is why some people feel pain in their forearms when curling). The heavier you go, the more the stretch, the more the associated discomfort. How do you fix this? You keep getting stronger (leading to increased rigidity of bone attachments and strength), and regardless of who disagrees, you keep drinking milk...because it does a body good and all of that shit.