Is it possible that the doctors were wrong?

Back on the 5th of July, I crashed on my longboard, and got some gnarly road rash. I went to the hospital and they wanted to x-ray since I said it hurt my left elbow pretty badly when I bent it. They did the x-rays and told me that I had fractured a bone in my elbow. They couldn't seem to tell me which bone exactly, and they splinted it with a plaster cast thing.

A week and a half later, I went to see the orthopedic surgeon to have a permanent cast put on. He looked at the x-rays and was unable to locate the fracture. He said that my left radius bone looked swollen compared to the other, but I could not tell the difference at all. He did not bother taking new x-rays. He removed my splint, and told me to try and straighten out my arm as much as possible. He then told me to try and rotate my wrist. These were both difficult and hurt a little, but I had been in a splint without moving my arm for a week and a half, and I felt that stiffness should be expected.

He put me in a new half-cast that was removable. I was told that after two weeks I should remove the cast 4 to 5 times a day and do 4 to 5 reps of straightening my arm as much as possible and rotating my wrist. I have been doing that, and can almost completely straighten out my arm now, and have no issues whatsoever with the wrist. I haven't been wearing my cast nearly as much, and am able to do basically all daily tasks, no problem.

Is it possible that the doctors were wrong, that there is no fracture? I mean, he couldn't even find it on the x-ray. I'm going back on Friday and he will take new x-rays, but I'd still like to get another opinion. Thanks!