First of all, be sure to take acetominophen (Tylenol) to reduce inflammation.
R.I.C.E. - Rest, Ice, Compression, Elevation. This usually applies a bit more to legs (at least, the elevation part) but it's pretty much true all over your body. Resting is important because you need to give the muscles (and even more so for joints) a chance to heal. Ice helps reduce inflammation and swelling. Compression reduces swelling associated with inflammation. Elevation reduces swelling by improving blood return from the area to your entire circulatory system.
Secondly, good form is critical. When doing the bench, you want your forearms under the weight at all times, perpendicular. This requires you to shift the weight lower towards your nipples as you descend. When you ascend back up, the weight should shift back toward your head. This way you're employing the chest muscles to a large degree, rather than the anterior deltoid.
Thirdly, another aspect of good form is the pinching of the shoulder blades. You don't have to necessarily actively pinch the shoulders toward each other, but your entire body (abs, back, legs, neck, etc.) need to be TIGHT. You need to be tight during the lift. None of this flimsy crap. The weight should not ever be moving laterally from left to right or vice versa. Tight.
The fourth aspect is strengthening the posterior (rear) deltoid. The EASIEST way to do this would be to hop on a rowing machine and row a solid 2 kilometers. (or whatever you can handle). You can also do this by lying on your side on the floor, resting on one elbow, and use your free arm to rotate a 2.5lb weight outward toward the ceiling (keep your upper arm locked against your torso, and rotate it so that your forearm & hand are the moving objects, basically so that your elbow is the pivot point. Your elbow will roll a short distance across the side of your torso.). Another method is bent-over rows, but I think a cable rowing machine is safer.