Strength Training with Shoulder Injury

I had an mri done and found out I have a rotator cuff tear in my left shoulder. It only bothers me when I'm sleeping or try to reach behind. The doc suggested surgery but said it may be ok if I don't have surgery - some people don't.

I haven't done strength training in a couple of months so that I could rest my shoulder but I want to start back up. I plan to do lower body but I was thinking about doing upper body as well - skipping the shoulder exercises and chest flyes.

Does anyone have experience with a rotator cuff injury.

btw - I know I should have asked my doc this - duh! But I did not think about it at the time.