I'm not an expert but I had a very similar experience after I broke my collar bone in high school. My pec on that side was bigger and my shoulder on that side felt weaker. When doing bench presses, I could feel that shoulder was limiting me more than anything else.
I finally started to get over it when a trainer suggested some exercises that targeted the shoulder area and I started using dumbells in each hand instead of the usual bar bench press.
The exercises the trainer gave me involved leaning on a pilates ball at about hip level with your feel on the ground/against a wall so that you're making a plank at an angle to the ground. Then, with a very light (2lb?) weight in each hand you go through 3x10 of what we called "I,Y,T" where you hold your arms straight at your sides so you look like the letter i. Then, straight out to the sides so that you look like the letter T, and finally extend them 'above' your head so that you look like the letter Y. You should keep your arms straight through the entire movement.
The other exercise started with the same position on the pilates ball and the light weight but you pick the weights up from the ground almost like you are doing a reverse bench and bring them to chest level. Then, while keeping your elbows bent you rotate at the shoulders until the weights are even with your ears. Finally, you push your hands straight "up" until they are above your head and you look like superman flying through the air. This exercise was also done in three sets of 10.
I just mixed at least one of these exercises in with each workout when I was going 3 times a week.
I think the dumbbell bench press should be obvious.
I started to notice that my shoulder felt better and my normal bench press improved after this. In addition, I no longer felt like the bench was straining my shoulder after heavy lifting. It finally felt like I was working out my chest muscles.