Milk stout and sweet stout are the same thing, just different names. If you have enough bottles, enter it in both. If the Bourbon and Vanilla are noticeable, then it will probably get dinged in the sweet stout category, but category 23 (specialty beer) is probably the best fit in terms of style. It depends on the competition and the judges, but I was docked SEVERAL points in my first competition on my saison, because the judges said it should have been entered as a Witbier instead. Apparently entering in the incorrect category causes you to lose a significant number of points.
"Give a man a beer, and he will waste an hour. Teach a man to brew, and he will waste a lifetime!" Bill Owen