I'm not a doctor and I don't play one on TV, but...
As I understand it a 'rotator cuff' is a system of muscles that move the upper arm up and away from the body.
Since a 'shoulder fired gun' actually sits on the pectoral muscle, I'm curious how a recoil pad could help.
It won't lift the gun for you, and even if it helps with fatigue it might encourage you to do something that you really shouldn't be doing and the result could be, as you fear, more damage.
Were it me, I'd lay off shooting and get the thing fixed while it still can be.
