Unsync iPhone from an iTunes account to transfer music to another

Every time I try to sync my music from my iPhone 4S to iTunes, a message shows up and says "Do you want to sync with this library? Your device is previously synced to another library. Syncing with this library will delete all your data. Do you want to continue?"

I made a separate user on my family's mac, so I want to transfer my phone's music to my new itunes library. How do I do it?