Could it be possible to dislocate a joint and have it go back in by itself and have no swelling?

Yes: It is very common in the shoulders.

Unlikely: It takes a lot of tissue damage to dislocate any joint. The ligaments and joint capsules typically need to be torn for a joint to dislocate and this will cause pain and swelling. It is possible for a joint to dislocate and spontaneously go back into place, but typically there is a lot of pain and swelling with that.