I'm a PT and have some general advice for you:
1. with ANY shoulder injury, avoid exercises past shoulder level..technically the shoulder joint has the least amount of space for the tendon to glide between the bony structures anywhere past 70 degrees.
2. ice takes 20 minutes to penetrate a big thick shoulder like yours..Either give it time and deal with the throbbing, aching, and then numbness or dont bother at all.
3. posture: sounds stupid but this is very important. If you slouch for most of your day, it puts your shoulders in a rounded position and makes your shoulder function in a less than optimal position..so sit up tall and dont round your shoulders. ...you're supposed to imagine pinching something between your shoulder blades. that stands you upright.
4. drop the weight while you are healing. even though you CAN do it, doesn't mean you should. back off a little...
5. which exercises to keep and which to lose: drop any exercise that is overhead for now. If you havent been stretching, start stretching the shoulders...I'll post a good rotator cuff stretch as a new thread. I can guarantee if you're a thick guy used to lifting heavy, its tight.