"If lip balm doesn't do the trick, you should consult a doctor"
Chapped lips can not only be a sign of vitamin deficiencies, but also more serious conditions particularly in children. Pellagra which results from a niacin or B3 deficiency is something that you shouldn't mess around with. It can lead to death if not dealt with properly. Another issue that isn't very well known is Kawasaki disease that primarily affects children under five and can cause heart problems if untreated. Both of these disorders have chapped lips as side affects although if you do more research there are of course other side effects that accompany them. (source)
If you have chapped lips constantly, make sure to check your chapstick for eucalyptus or camphor, both of which actually dry out your lips instead moisturizing. (source) If you can't get your chapped lips to go away, it would be best to bring it up with a doctor and to not take it lightly. It may be an easy fix such as a multivitamin, or something more serious if you have other symptoms.
If you want a great chapstick I live and die by Burt's Bees chapstick, it's the only thing that makes my lips feel happy. I swear I have at least one in each purse, my backpack, and my car. Do you have a solution you use for chapped lips?