By setting, do you mean tying something wooden to a broken leg or arm in order to keep it stable? If so, yes, it's possible to do, if you can handle the absurd pain involved in such a thing (I once broke my arm at an angle and had to straighten it for X-rays. Let me tell ya, that was arguably the most painful thing I've ever done to myself because it felt like I was breaking my bone more).
If the fracture is in your arm, it will be more difficult to do it. I think I would much rather break a leg than an arm because with my arms I can make splints / crunches, and evaluate my leg to see if the bone is sticking out of my leg. It's much harder to evaluate your arm when you only have one hand to feel around with, and it is very difficult to tie a sling around yourself with just one arm-- you have to use your neck and teeth to help you, and I doubt it would be very tight. Still, as long as your hand functions you can still use it to help assist you in making a sling, but I imagine it would be a very painful experience.
People do pass out in situations like that from the amount of pain and the whole "OMG my arm is broken" shock they experience. There are people who do quite literally pass out when they realize they are bleeding--even if it's not a serious wound-- and it is an entirely mental thing. I think everyone who gravely injures themselves has to fight for consciousness when they first realize they are injured, which is why medics are trained to keep injured people talking. The brain naturally wants to start shutting stuff down to preserve itself, so someone who has to treat their own serious injuries is going to have to be able to know they have to maintain consciousness and have the willpower to do so.
Even if you've broken a bone, you can move it if you really want to unless the muscle has been torn. Bones are not what moves your arms and legs-- it's the muscles. The majority of people won't move a broken limb because it hurts so much to move it, but if they want to they can-- although they shouldn't because they risk potentially damaging themselves more.
As for things like popping your own joints back into place without assistance, yes that is also possible. I've seen it (when I was a teenager I used to do some sparring in Tae kwon do tournaments, where someone might occasionally hurt themselves by dislocating a shoulder) although it is by no means easy. Although some movies are ridiculous, you'd be surprised how much you can actually do to treat your own injuries if you know what to do and can keep a level head-- I once performed the heimlich maneuver on myself when a dentist removing my wisdom teeth dropped the tooth down into my throat. I think the most "Hollywood moment" thing I ever learned to do in the Army related to treating injuries was using a potato chip bag to dress a punctured lung.
I wasn't a medic in the Army, but I was an infantryman with combat lifesaver training. I never had to make a sling for my own broken arm though, I'm just guessing based on what I know from personal experiences with a broken arm and the training I had about making improvised slings and splints.