I just experienced the same problem.
I updated my iphone to 6.1 and just after I did it, I realised I neither had the text message alerts nor the music/youtube sounds. I didn't have the little +/- squares for the volume either. I tried plugging in my headphones, taking them out etc, did this a several times - nothing. But then this worked:
I put my iphone on my dock (speakers) and hit the play button. The speakers were working and the music was playing, so i took the iphone out, then put it back on the dock, hit the play, and while the music was playing, I took the iphone out again. And suddenly the music was playing on my iphone.
It just has to realise that there is an "iphone" option on that little square and triangle sign (sorry i don't know what that is called) just next to the volume line. When it wasn't working, the only options I had there was my airport express and my headphones - now it is fixed, it is on the "iphone" option. There is a little check next to it.
It was the stupidest thing I have done to fix a techonological item. But oh Apple, it worked.