Have to be careful with gyms. I injured my shoulder doing weights over twenty years ago and still have trouble with it.
This is a very lame excuse. You can do 100 different things without compromising your shoulder. Try cardio. Or just wight lifting with very light weights. Or group classes.
Warm up for every workout. Allow 72 hours recovery between lifts. I.e. if you bench press on Monday, don't do it again until Thursday. Do legs instead. I do squats on Monday, bench on Wednesday, deadlift on Friday.
Progressive overload is important but don't add more than 5lbs when you're moving up. Don't ego lift, there's always someone who can lift more than you; you should only be competing with yourself.
Always have a spotter or at least safety pins if you're anywhere close to your max weight or reps.