@Illych - You're right that the longer you wait to get it put back in place the more it's going to hurt. It doesn't hurt at first because the intense pain causes the body to release endorphins to lower pain and shock, but once the endorphins wear off then it's going to hurt a lot. This is why some people resort to doing it themselves.
You can try the method you mentioned where you let the arm hand and hope that the muscles loosen up and it will quickly pop back in, but I wouldn't recommend it. Sitting in the waiting room isn't fun but it’s best to have it done by a professional. To ease the pain you can ask a nurse for a small dose of muscle relaxants.