When Should I Start Moisturizing After a Medium Chemical Peel?

Sunscreen daily and every 2 hours when sun exposed; I generally recommend only moisturizing if necessary in between to speed the peeling process. Sunscreen is very important, though. Best of luck with your results.

Immediately! The more moisture, the better! It will help the healing process.

I have all of my patients moisturize and treat their skin with Melarase after chemical peels to provide physical sunblock and skin lighteners. Raffy Karamanoukian, Los Angeles

You should start immediately after your peel.  The moisturizer allow for the skin to heal quicker.  

Dr. ES

You can moisturize right after getting the peel!With all peels, skin can become sun sensitive afterward, why we always recommend that patients, after having a peel, avoid the sun and wear daily broad-spectrum sun protection. For lighter peels, an over-the-counter topical broad-spectrum sunscreen works best. For deeper, more intense peels, we recommend that patients avoid direct sun exposure for several days to two weeks.