So I have an old injury (a partial tear in the labrum of my left shoulder) from several years ago that had stopped bothering me. A few weeks ago, when I tried doing ?push presses (from the NROL4W, stage 4), that shoulder immediately flared with pain, and hasn't let up since even though I haven't done them again. Now, anything I do that gets my arms over my head in a torqued way (Cuban snatch, wide-grip lat bar, etc) hurts during the weight-bearing phase. The outer aspect of my wrist has just started to hurt "in company with" the shoulder (I think I must be favoring the shoulder by doing something different with my grip on that side).
So, do I need to stop doing all weight-bearing exercises that use the shoulder (pretty much everything that isn't leg or core work)? If so, for how long? Do I continue to work through the pain and hope it heals on its own? Do I do my usual routines but with half the weight? Do I use dumbbells for everything, and use a lighter weight only on the left side?

That must be really frustrating! Kim's right. Go make an appointment to get it checked out. Never work through that kind of pain. It will only cause an acute condition to become chronic and encourage a second injury to develop from overcompensation (I'm thinking about your wrist here).