iTunes is giving me some issues on my iPhone to new laptop and vise versa

I got a new laptop recently, but I still have my old one. I got iTunes to listen to the Reputation album that I uploaded to iTunes on my old laptop and iPhone because I have a CD player on my old laptop. I used the same Apple ID on both laptops, but on my new laptop nothing in my music popped up! I plugged in my iPhone and iTunes did notice that it was there, but if I tried to sync it would say this will delete all the music off my iPhone which I absolutely don't want. Unless I can restore it somehow after iTunes on my laptop deletes it is there any other way that I can get my music on here? I even logged out of iTunes on my old laptop and that didn't work! Please reply!