Do you have more that one Apple ID? I've ended up with one for iCloud and one for iTunes and App Store. If you go to [settings] from your device, then click [itunes & app store] is the apple ID you've registered with iTunes there?
Within the iTunes Store app, click [more] then click [purchased] then click [music] - it should be there with a little cloud symbol and an arrow - this means it's in your account cloud but not downloaded to your device. Click [download all] and it should then download to the device. :thumbsup: