I have a torn labrum in my right shoulder (confirmed by MRI), and I believe I now have a tear in my left shoulder.
For my right shoulder, I had to avoid all overhead pressing, most other shoulder work, certain benching exercises and also ease up on pullups and some biceps exercises. I iced it, used Aleve, and sought chiropractic care involving adjustments, massage, muscle stim and ultrasound. After six months, I no longer had pain/problems with my right shoulder. In fact, it feels better than ever.
Now I need to go back for treatment on my left shoulder and hopefully, it will react the same. I do some overhead pressing (implementing it back into the program six months ago), and it has not caused too many problems (some days I have pain in the left shoulder).
I didn't want to have surgery because it wasn't bad enough to necessitate it at the time. A friend of mine is a PT, and he said that if the pain is so bad that it keeps you up at night or causes problems with sleeping, that's when you should elect surgery. Otherwise, if ice, ibuprofen and massage or other techniques work, it's not worth having surgery as many people who lift weights will have a torn labrum.