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.
Eyes: Blue. I'm actually really loving this primer under matte and liquid matte lipsticks. My lips are dry and cracked looking even after exfoliating and putting on lip balm. Most lip primers keep my lipstick in place but don't do anything to make my lips look less flaky and gross.