Cannot delete songs from iPhone, sync also not working

I purchased a new iPhone 5s two months ago.

After transferring all my songs from iTunes onto my iPhone, I found that there was very little or no free space. I attempted to delete some of the songs by plugging in my phone and deleting the ones I didn't want. However, after ejecting, the songs remained on my iPhone. I tried twice more, and on the final time, out of frustration, I deleted all the songs from my iPhone. This time, the songs I had originally intended to delete were gone and the music was still there, contrary to my deleting all the music.

Now when I go to plug in my phone, it shows in the 'storage used' bar that there is no music. However, when I open my phone, the song names are still listed but none can be played. Additionally, when I try and go go to 'manage usage' and click on music, the settings app crashes. This happens every time.

Finally, when my phone is plugged in, it will indefinitely have the rotating arrows next to the name. When I cancel, it will then indefinitely say 'cancelling sync'.

So my next step is to restore the iPhone, but I was hoping someone here would have some insight. If i restore, will I keep my notes, photos etc from backup?