You could either be suffering from contact dermatitis or from allergy
to some food. You should get an allergy
test done, either a skin test or RAST, to know what you are allergic to. Contact dermatitis could be due to tooth pastes, mouth cleansers, spoons, cups, glasses, food items, cosmetics, shampoos, etc, basically anything that comes in contact with your lips.
Another possibility is eczema. Herpes infection is another possibility if there is a history of kissing or sexual contact.