If a shoulder is dislocated, you won't be able to move it, you won't be able to lift your arm.
Wrist/hand/arm breaks: Obviously, if there's any disformation (that isn't just swelling). Is it swollen? Bruised? Tender to the touch? Hurts to move? Can you feel anything 'crunching' when you move it or press on it? When you press on it, does it feel like broken eggshells under the skin?
I've walked around on broken bones for weeks before, thinking it's just a sprain or bruise. Don't do that ;) But taking care of it at home for a few days until the swelling goes down is preferred (unless the bone is coming through the skin!!)... I've broken multiple bones, and I'm a former EMT.
Really, an X-ray is the only sure fire way to know. I would ice and immobilize it for at least a day or two before going to the doctor, since if it's still crazy swollen, they won't be able to take a clear X-ray anyway.