Face was already clear but started peeling again after applying Cosmelan 2 one week after Cosmelan 1 treatment. Is this normal?

Yes, it is very common to experience more peeling after staring Cosmelan 2 maintenance cream. The perioral area around nose and mouth are areas where we commonly see this happening. I instruct my patients to avoid this areas until irritation is better, normally a couple of days.The patient should actually expect peeling on and off all during the treatment. Remember to listen to your skin if you are excessively irritated you need to rest for a day or two and then resume with your regimen. We keep very close communication with our patients undergoing Cosmelan as every patient will react different to this treatment. Stay in touch with your provider. 
Best of luck, Dr Obaid.

This is difficult to answer without pictures. After Cosmelan, I recommend a chemical peel or lasers for long-term improvement. I recommend following up with your cosmetic dermatologist about after care. Best, Dr. Emer