believe me man, you WILL regret this, and your gf may even too.
why? cause guys naturally look good with hair, and they become less atractive the more they get older if they have none.
and lots of girls think it's really grooows to see a guy with no hair. lots of girls LIKE guys with hair.
PS: if you shave now, you'll have to be shaving everyday for the rest of your LIFE!!! why? hair always grows back faster and thicker the more you shave.
your girlfriend sucks man. it might even be a way to dump you, and then make fun of you later!