I'm under 18, so Facebook "protects" my information, and no one can see my "About me" unless they already have me as a friend. A lot of developers are adding me as a friend because of a contest I recently competed in. However, I want to redirect all of the developers that I do not know to my LinkedIn profile. Is there a way to add a public link to my public Facebook profile?
There is no way around Facebook's security features for minors. You can modify your Timeline Cover or profile picture but those changes will be visible to everyone.
However, none of this matters because people will still add you as friends - they'll just look over it. Thus, simply reply to them privately explaining that you would like to keep Facebook for personal contacts only & connect with them professionally on LinkedIn.