Refractory chapping may be one manifestation of
herpes-
labialis infection. Topical medicine will often be required
for this. The most commonly used would be Silica Gel or Topical Acyclovir Cream.
Before embarking on a course of therapy, however, it would be wise to consult with a dermatologist, for if the infection leads to actual wounds, additional therapy, such as occlusion therapy, may be warranted.
Good luck.