"Sour tooth" sounds like a derivative from "sweet tooth" - it sounds a little unnatural to say "sour tooth" (ie. you like lemons and such), but it's perfectly understandable. It can also mean an infected or rotting tooth, but that's probably not what you were thinking of.

The opposite would be to have "sweet tooth", one who loves to eat a lot of sweet foods and treats such as candies, chocolates, cookies, etc. One with a 'sour tooth' wouldn't like those things.....me! Hahah