Working out around a right shoulder injury

My questions: What kinds of exercises could help with the shoulder? What kinds of exercises either with machines or free weights could help to build the upper body without aggravating the shoulder?

More detail: When I was young and working out I tore or stretched some ligaments or tendons in both shoulders that healed themselves and in fact I got back to working out then with no pain, no limitations, no problems. Now, at 57 I'm working out and I find that many exercises where the shoulder is in use aggravate the old injury, but only on the right shoulder, and only on the very top of the shoulder a few inches above where it connects to the upper arm. I have no issues or pain with the left side what so ever. The right shoulder doesn't hurt in any area but what I can guess is near the bone that starts where the collar bone ends. That's not to say that it feels like a bone injury per se; it's more irritating than debilitating, meaning I can do all the exercises OK but with some pain. And, the pain didn't appear right away when I got back into the gym about a month ago. So, I'm not entirely convinced this is related to the old injury, but I don't know what I could have done to the right shoulder or when.

It's only two days since my last workout and the pain is already at least a third to halfway gone when moving the shoulder. During my last workout, I found that 5lb. lateral raises didn't seem to aggravate it (I'm used to using 15 to 20lbs with slow steady movements and no pain). The bench press, tricep bench press, and standing barbell shoulder press did irritate the shoulder, in fact it was painful enough that I decided not to push through the pain but rather did fewer reps.

I am looking for shoulder exercises I can do to build the muscle in and around the shoulder to strengthen and support it as it heals. I am also looking for ways to do upper body exercises with weights so I can continue to build the other upper body muscles without aggravating the shoulder or stalling the healing process.