How do I sync ALL of my music?

Yesterday I upgraded from an iphone 5 to an iphone 6s plus. my iphone 5 has 1100+ songs on it. About half of which I purchased through iTunes, the other half were loaded from CD's. All of the music was on my phone- but not my computer. My old computer died, and my new computer does not have a CD drive, or any of my music on it. I backed my phone up to my computer before I bought my new phone. iTunes told me there were 21 songs that it wasn't able to transfer, and they were songs I didn't care about losing.

When I synched my new phone to my computer- i ended up with only 500ish songs- only the music I had purchased through itunes! The rest is not showing up in my itunes library, though it is all still on my old phone. How do I transfer the music I had uploaded from CDs to new phone? I don't have the ability to manually load those CDs onto my new computer.

Please help!