non itunes-purchased songs on iphone 5s won't transfer onto new computer's itunes
So I have a bunch of mixtapes, audio files, unreleased songs and CDs on my phone but since I downloaded iOS8 (almost a year late because I never download iOS immediately), none of these songs are in my itunes (added note - I just got my first Mac, my PC worked fine with iOS8. go figure) and I'm scared to try the "sync music" check box because when I click it I get the message "Are you sure you want to remove existing music, movies, TV shows, books, and tones from this iPhone and sync with this iTunes library?" because that sounds like I'm going to get rid of 2000+ songs just because I didn't purchase them via itunes. Is there a button or something that shows ALL music, not just purchased that I'm missing or...?
TL;DR - lots of songs on phone; not many songs on iTunes; don't know how to get non-iTunes purchases onto iTunes/computer
iPhone 5s, iOS 8.1.2