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.
I have a recurring lip problem. My lips start off really itchy and they feel like they are sunburnt and its stings around the lining of my lips. They then become super red and the whole outer are of my lips look red and swollen. Sometimes I get crusty stuff on my lips but only sometimes. It sometimes feels as if my lips are sweating.