Is this music you have purchased through the iTunes Store?
If so, then you can download it directly to your phone as follows (assuming that the Apple ID you have signed in for the iTunes & App Store on the phone is the same one you purchased the music under):
Click on the iTunes app on your phone
Click on More
Click on Purchased
Click on Music
Click on "Not on this iPhone"
Click on "Recent Purchases" or "All Songs"
You will see a list of songs that can be downloaded. They will have a little cloud with a down arrow next to each one
You can selectively download the ones you want by clicking on the cloud next to them, or you can click on Download All in the upper right-hand corner
You need a third-party program like one of those listed her to get it from the iPod to iTunes. Then you can sync to iPhone