When Should I Start Moisturizing After a Medium Chemical Peel?

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.