so I have probably the most "newbie" question ever, but I don't understand why I have to either be on wifi or it comes up with a message saying I have to access my cellular data to listen to my own music? My device is an iPhone 6.
Go to Settings/General/Storage & iCloud Usage and check to see if Music is an option. If there isn't anything there, then it's not on your phone. With iOS 9, the line between the cloud and downloaded has been blurred, so it can be slightly confusing as your purchased music automatically shows up under My Music.