It seems very unlikely that chemical peels
could be contributory for your skin dryness currently. Normally skin may peel for one to four weeks after chemical peel session depending on the concentration of the peel and whether it was a superficial peel or a deep peel. The dryness of your skin right now could be due to cold
dry weather. Use a mild cleanser, sunscreen and a hydrating moisturiser to keep face well moisturised. If the skin is flaking too much, a mild steroid
could be used for few days to alleviate dryness.
Hope that answers your query.