Q: itunes

I recently bought a Macbook Air and I have an iPhone 5s... I can download music from the internet onto my mac and into my iTunes library but it won't transfer onto my phone. All the music listed on my phone is only listed in my iTunes library when my phone is connected via USB. When my phone isn't connected, all my music that I downloaded is in my iTunes but none of my pre-existing music from my phone is visible. When I try to add my music to my phone I get this notice: "Music, movies, TV shows, books, and tones synced to “Kylee's iPhone” from other iTunes libraries will be removed and items will be synced from this iTunes library." I used the same iTunes account as before, just a different computer... could someone help?