There is a Summer / Autumn / Winter / Spring pattern in the Temperate zone, also affecting the Desert and the Grassland climatic zones and, a Wet / Dry pattern in the tropical north which includes the Equatorial, Tropical and sub-tropical zones.
Most likely, your lips are suffering from excessive dryness, or chapping. Actually, picking at them and peeling off the skin can worsen the situation, as this can make the dryness worse. It would be better to try applying a good lip balm or lip moisturizing lotion. This should help you break the cycle of dryness and peeling, but only if you can refrain from picking at the skin in the meantime.
If you have a pimple on your lip DON'T CUT IT OR POP IT WITH A NEEDLE. A doctor may do that for you, but that is because they know how. If you don't squeeze all of it out, you can end up pressuring the oil lower and will result in a blackhead on the inside of your lip which looks like the nastiest swollen case of herpes you can imagine.