try doing partial reps with more weight and see if that helps....its not ideal but the reduced stress on the shoulder may allow you to still make gains and protect yourself.
Try partial bench presses in the rack or benching off the floor.
If these partials still cause a great deal of pain....stop...even though i know that sucks...until you figure out what is going on....no sense in risking permanent injury.
It sounds more like a bursitis...but of course it is hard to tell without actually seeing you. good luck.