Chapped and darkened lips both indicate people may be suffering allergic reactions to an ingredient in lip balm. Ceasing to use lip products and seeing if the symptoms improve is a good first course of action.
Menthol and camphor are two ingredients known to dry out lips, so avoiding them can make lips more hydrated. Lip products that are more than two years old may cause lips to darken but usually only if the ingredients have expired or were very low quality. Failing to use lip balm that includes sunscreen when outdoors can cause chapped lips, and consuming coffee or smoking cigarettes can darken the lips, so lifestyle changes may improve chapping and color problems.