I know it's shallow but my girlfriend's face is messed up and I'm just not attracted to her anymore. How to break up?

If you ask me, the messed up one is you.

You go to her house and apologize profusely for being a jerk. You tell her even though she is a great girlfriend that you are scum and you are breaking up with her so she can find a real boyfriend who will treat her with the care and respect she deserves.

They make a lot of designer bags to put over her head.

Just tell her you're too shallow to be her boyfriend and you hope she finds someone who respects and cares for her.  Do her that favor!!

For what ever reason you no longer find her attactive .. There is no reason to be mean or hurtful about it. Be kind, be gentle but be truthful by telling her this is just not working out.

I decided to date your girlfriend because you are a jerk

I find Bikergirl Anonymous's answer to be the most practical.

We don't really know if her face is the problem or if your general lack of interest in her has somehow become associated with her looks.

(So you may or may not actually be a "jerk.")

So as Bikergirl said, "There is no reason to be mean or hurtful about it. Be kind, be gentle but be truthful by telling her this is just not working out."

And don't tell her it's you, not her. The reality is that not all relationships are going to last forever---and it's nobody's fault.

"There ain't no good guy, there ain't no bad guy.  There's only you and me and we just disagree."

https://www.youtube.com/watch?v=b2ff8qXa248

(And I was pleasantly surprised and delighted by watching the ad that played before the actual video of Dave Mason singing We Just Disagree.)

What was her face like when you met her?

If you took her up as your girl for shallow reasons in the first place then you are not only an ass but you are holding on to this girl under false pretenses. Do her a favor and get lost.