Swmmers shoulder? how long does it take to heal?

I have rotator cuff tendinitis. I was told to take mobic everyday, keep it in a sling for 10 days, and to ice it. Doc said to do gentle pendulum exercises at night to prevent frozen shoulder but I need to rest it completely for 10 days. If it doesn't heal by then I have to get an mri to check for a tear. Doc said that this was unlikely. How long does it take to heal? Can I work out in my sling? I have qualifying meets in January and I need to keep in shape. Also, could I have a tear if my shoulder is a little weak and it's grinding?