You seem to be describing damage to your acromioclavicular joint, (a/c joint). This is where your collar bone, (clavicle), joins to the acromion process, that projects over the top of your shoulder, from your shoulder blade.
This is an easy joint to injure, and if it is injured, rest is really the best answer. Ice for about 20 minutes, 3 times per day, will also help to speed the healing.
Make two fists, and put your knuckles together; that's what the a/c joint basically consists of, two bones that butt together, and are held together by ligaments. A shoulder separation occurs when these ligaments are torn or damaged, and the two bones comes apart.
If we are dealing with some damage to the a/c joint, then continuing to train is a big risk. As others have mentioned, it's just far too easy sometimes, for a small injury to turn into a big one, even a permanent injury. You really don't want that, nobody does.
If you really need to keep on training, then all of your upper body lifts will have to be light, and you should not be doing any exercises that cause any pain. Any kind of strain could turn this from a small injury into a big one, instantly. If it were me, I would stick to light lifting for at least 8 weeks to be safe.
Most problems in lifting can be solved by either pulling harder, or pushing harder.