How to get my iPhone to download music from my iTune Library?

I recently got a new laptop and I'm trying to download some music onto my iPhone. I tried dragging it into my phone but whenever I do, the song I'm trying to download shows a red circle with a slash in the middle. I also tried making a playlist and syncing it to my phone but it takes me to manage my music and a message pops up that says that my phone is used in another iTunes library and if I'd like to erase and sync. What can I do so that my new laptop can download music without it being such a hassle?

Your iPod is connected to another library. You need to restore it. Start over sorry.