I am rehabing an impinged rotator cuff, and have not shot period for several months. The Doc said, ignoring the pain caused by the impingment, would eventually end in a tear. I think, their diagnosis is correct and have committed to following their instructions to strengthen the rotator cuff and avoid any further stress to that area. It feels better after several weeks of limited exercise for the rotator cuff. It may sound strange, but exercising the deltoid muscle is exactly what I should not do, as it makes the problem worse.
I am not qualified to give advise, but if it were me, I would follow their advise, or get a second opinion. Trying to live with the pain, or working through it, just wasn't working. I tried that for two months.
Good luck, Barry