This sounds like humorous advice. It means "Don't let anybody else use your comb because you might pick up lice or a disease." Though nobody has ever offered me this advice before, I've heard similar things used when people are trying to be funny.
That sounds right to me, Strolling Girl. What makes it funny is that this caution comes after the statement "Live fast, love hard, and...". Living fast and loving hard are not the sorts of things that we ordinarily associate with caution.