"Outta" is slang for "out of." It's rarely used in written English, but here's how some people might say it: "Let's get outta here." "Hey Mom! We're outta milk."

I'm a native English speaker who loves to figure out what is meant by song lyrics. The song writer Jordan Klassen lives where I do but I hadn't heard his music. Thank you for introducing it to me! I was still having a very hard time figuring out exactly what he means, so I actually ended up sending him a message on Facebook regarding this. I'll let you know if he replies. My interpretation of those lines is: "I have prettied myself with ball and chain"- He has tried to make himself more desirable to the person he is writing to by making himself seem less free (probably less free in how he behaves and approaches life rather then literally less free in movement) "With a refugee in my old name"- It really sounds like he's singing "refuge" not refugee, even though that's what is listed on lyric sites. I've asked him to clarify this as it really changes the meaning. Saying that, this is a song that if you asked 10 different native English speakers what it meant you would get 10 different answers because it's very vague. Hopefully Mr. Klassen will return my message and clear things up for us!