You could go either way, bvkerbear. Your hair looks just fine without them, but there wouldn't be much harm in getting them, provided that they were sideswept and long enough.

The type that fall flat across the eyebrows would not flatter your face shape, but long, sideswept bangs would. A word of caution, however: most people with bangs just grow them out eventually anyway. Also, it will take away some of the thickness from your hair, seeing as part of the length in front will need to be cut off to create bangs. And your mother is right that they will get in the way and you will have to keep sweeping them out of your eyes. If none of this bothers you, then I'd say go for it. It's just hair and it grows back. God knows we've all done worse to ours at some point.