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.
What are blue lips? Blue lips occur when the skin on the lips takes on a bluish tint or color. This generally is due to either a lack of oxygen in the blood or to extremely cold temperatures. When the skin becomes a bluish color, the symptom is called cyanosis. Most commonly, blue lips are caused by a lack of oxygen in the blood. This may happen when you are at high altitude or if you are choking, or it may be due to chronic underlying conditions such as lung diseases or chronic heart defects.