Blake, your first priority must be healing. If that means no lifting for a day, a week, a month, or a year, so be it. Not healing before resuming your previous strength training is very likely to be penny wise but pound foolish.
You need to check with your doctor, but in many cases, if it doesn't hurt, it's OK to do, and if your doctor agrees with that advice, then you need to do a simple experiment to see what your shoulder will and won't allow.
Another thing to mention is that if your injury is only on one side, you will still maintain much, although not all, of your strength on the injured side by continuing to train the other side. I believe this was mentioned in one of Pavel's books although I can't remember which at the moment.
If holding a weight overhead doesn't bother you but pressing does, consider movements that put the weight overhead ballistically, or a movement like the getup where you could use the other arm to assist in the floor press.
When you are in pain, your doctor's advice should be your primary guide. And if your doctor doesn't understand your desire to return to training as soon as possible, consider finding another doctor, one who specializes in athletes.
Best of luck to you.
-S-
