My iPhone 4 won't sync other music only iTunes?

Hi, So i got the iPhone 4, The white one for christmas and it only automatically syncs music from iTunes store, not from sites or albums that i download to my mac. It really frustrates me because I would love to stop spending money on the iTunes store and just get my music from albums that i downloaded into my computer. I don't know why I have this problem. It's not the iPhone 5, or 4s just the 4. My mom has no problem downloading hers from albums or music she got form sites, but mine syncs really quickly and the music doesn't show up. Any clues or things I should try to fix this problem. Also I have iCloud if that has anything to do with it. And i haven't tried restoring it because i'm scared it will erase everything and not be able to ever get it back. I think I have had updating it but it still doesn't work. If there's anything that i must try to fix this problem, Please TELL ME! L Thank you very much.

Maybe try managing the music and videos manually. To ensure that you don't lose the music, just use sharepod and backup the music. You don't need to restore device at all. After ticking 'Manually mange music' it should work for you. You have to do this for each device manually