There is nothing worse than a shoulder injury...this can prevent you from performing nearly all upper body resistance training. It is very important to ensure that you train in a safe manner in order to avoid further injury.
I actually train a handful of people with shoulder injuries (they are really common...particularly chronic ones in older clients). This is because the shoulder is an extremely unstable joint.
The main things to watch out for in an injury prone shoulder are overhead exercises (eg. shoulder presses) and shoulder isolation exercises (eg. side lat raises, front raises etc.).
Rotator cuff exercises using a resistance band can be extremely effective in building up the supporting muscles of the shoulder joint in order to avoid further injury. In addition to this, certain back exercises that recruit the rear deltoids (eg. lat pulldown, pullups, seated rows) may further assist the stability of the shoulder joint.
I highly recommend that you have a professional personal trainer prescribe a safe and effective program for you. For more information on my personal training services, click here.