Probably impingement syndrome, but it could be a deltoid strain or infraspinatus (less likely but possible). There is also a possibility that this is pain from one of the muscles attaching to the coracoid process. Finally it could be something to do with the long head of the biceps tendon. Going through them systematically and massaging out the tightness will let you know if that is the case. Don't miss coracobrachialis.
Massage all muscles that connect to or near the affected area on a daily basis, being sure to focus on separating the fascicles. It won't feel very good at first. You should also probably consider not benching while you try and fix this.