How to transfer music from my iPhone to my iTunes on my new laptop?

I downloaded music from youtube onto my iTunes using my old desktop computer, which i then synced onto my iPhone. I now have a new macbook air and i downloaded iTunes but only the music i purchased from iTunes is showing up in my library. I'm not sure how to get the music from youtube thats on my phone onto my iTunes library. How do i do this without deleting all of it? Also, is there a way i can do it without having to access my desktop itunes library? I'm on vacation and only have my phone and new laptop.

You have to download the new iTunes for iPhones

Hi, 4Videosoft iPad to Mac Transfer Ultimate will help you transfer music from iPhone to your new MacBook Air's iTunes. It supports iPhone/iPad/iPod. It's very easy to use and see the following steps:

1.it's necessary to download and run the program on your MacBook Air

2.connect your iPhone to the program via USB cable. In the left panel, you can see the all iPhone files

3. Check your iPhone music files and check "Transfer to iTunes" option, and then click "Transfer" button