Suggest a potential muscle tear (rupture) that never quite healed almost a year ago. Worse case, a rotor cuff..but let's think positive and not go to that extreme. Might try and work around the exercise that give pain. Also keep the shoulder area warm, evn applying a heating lotion/rub/stick on pad before and after a workout.
BB Benches can bring on some problems for a lot of guy's. Even with experienced lifters. DB benches, though not always a cure all, allow a more natural curve/phase to bench pressing. So might suggest starting with a moderate DB workout, rather than a BB. If your not doing that already, that is.
Personal view: I prefer dips over BB bench work. Second to dips would be DB bench/incline presses. A better pec exercise is the Pec Deck. Followed by DB flys, with a slight bend to the elbows. Don't have to go to the extreme with too heavy a weight. Good Luck.
Side Bar: Favorite, for me, is the Bent Arm Pullover & Press for chest, lats, delts, triceps and even abs. A true mass builder and compound exercise. I prefer DB's. BB's as a second option.