Could a nose job help my low lip-line?

The nose bone (or cartilage) between my nostrils slants to be like half a centimeter from my two front teeth, maybe a millimeter. (I can feel the bone when I touch my teeth). It’s about where my labial frenulum was before I got a frenectomy a couple weeks ago.

So I have a low lip-line, meaning you can barely see my teeth when I smile and my upper lip barely moves when I talk. The middle of my upper lip is forced down by my nose, unable to move. Kinda like this, for lack of a better image: http://www.kingswayortho.com/images/lowlipline.jpg
It makes for a less-than-pleasing smile, despite my straight white teeth.
I wanna know what can solve this. Can I get the cartilage cut or moved up? Do I have to take off part of my lip (I want to grow a beard, and that probably will interfere with facial hair growth).