Breathing problems, fluid buildup/retention, permanent disfigurement to the breast tissue, shoulder/back/chest pain, broken/bruised ribs, etc.
The percent chance of each varies, and is affected by whether or not you're binding correctly. If you are sure you are wearing the right size and you are not wearing it too long, then you should probably see a doctor to rule out other issues. Chest pain and tightness generally isn't a good thing.