The same thing happened to me. This only started happening after I updated my itunes.n
I tried to sync my music specifically, but couldn't do so because I didn't want to delete all of my music and re-add it all. So, I did the simple sync (the button on the bottom right hand corner), which took only a few seconds. Then, I dragged the music I wanted to my iphone bar on the top right side (what you would normally do).
Since I couldn't find my music on the list when I looked through it, I pressed the "autofill" button near the bottom right side. At first, the music comes up grey with the circles on the left side, but if you wait a couple minutes, it automatically downloads and transfers.
This might not work for everyone, but its worth a try (and its better than deleting all the music on your phone).
Hope this helps!!