Westell, I got hurt at 16 playing hockey. My cup didn't hold all my junk and really only protected my balls. While I also piss from 2 holes, I was born that way, and only recenly got that repaired. I have a son who had to have his redirected, it came out the bottom. While talking to Urologist, has asked to look, and with a local anestic, he opened me up. Pissing is easier and doesn't spray. Also, when I cum, if I have a big load, it would sometimes hurt. Not any more.
The injury to my penis wasn't that it popped or broke, but caused it to bend to the right afterwards due to the cavernosa being damaged in an area. I bought a traction device to lengthen a smaller penis for some guys, but with moderate tension, it straightend out. As far as your doctor is concerned, I would look for a new guy, and keep looking!! The doctor who handled both myself and my son was in sports medicine too, and has seen injuries like this before....check that out.
Only thing I am wondering though, if your broke it masturbating, how hard were you pulling? At 23, masturbating should be a big and healthy part of your life right now, and seeing that you are struggling, for your esteem and well being, keep looking for some good help. Best of luck to you too!