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.
While most of us don't think about this very often, you can get a sunburn on your lips just like you can anywhere else. This is the reason that so many of the lip balms that we use contain sunscreen, which you might not have even noticed. Dry and swollen lips can certainly be a sign of a sunburn, but it could alternatively be a sign of something as simple as chapped lips from being too dry and perhaps having gotten some wind burn or other irritation.