How to download songs straight to my iPhone 5c?

So on Friday I got an iPhone 5c for my birthday. And I can't put any music on it using iTunes because my computers broken. So I don't have any music on my phone. What I was going to do is download music using youtube but my iPhone doesn't let me. So my question is how can I download music straight to my phone without any computer? Is there any apps that work? (I've tried a few apps and none of them work)

Log into iTunes on your phone with your Apple ID and account balance or payment method. Purchase apps and music directly and it deducts from your balance and they download right there. It will sync copies of purchases to your PC once it's back up and running. Best luck.

Spotify

From itunes on your laptop

Try Spotify. Best Music streaming app out there.