Will a chemical peel work for reducing cheek dents (festoons)? (photo)

From the photo provided, it appears that you have malar creases, i.e. a diagnonal linear depression separating the lower lid region from the true cheek region--a situation that gives rise to the appearance of festooning of the lower lid region. I had the same problem myself, which I treated in my Israel satellite facility (where a far greater number of regulatory agency approved fillers are available) with the use of Teosyal Redensity, a filler that possesses little tendency to give rise to the unwanted bluish Tyndall Effect when injected superficially under the crease to elevate it and to establish a smoother, more natural and gradual transition between the upper cheek and lower lid regions. In my Manhattan office, I would opt for Belotero Balance for this purpose. It is difficult to say from the photo, but it is possible that some additional enhancement of the cheekbone regions with a volumizing filler, such as Voluma XC (NY) or Stylage XXL (Israel) may provide further lift and stretch to soften the crease. A chemical peel will do little for this problem. Treating this region is not to be left to the hands of novice injectors, so be sure to seek out consultation and treatment by a board certified aesthetic physician before proceeding. Best of luck.

What you are describing in your photos are known as malar festoons, which can be a difficult problem to treat.  This area is neither eyelid skin nor true cheek, but an area susceptible to periodic swelling associated with salt intake, allergies, fatigue, etc. Sometimes volume expansion of the cheek with Voluma can be helpful and at times a surgical solution, but deciding on the most appropriate treatment for you would require a consultation. A chemical peel is not likely to help this specific problem and given your skin tone may cause other issues. 

A combination approach would give the most improvement with fillers (Juvederm, Radiesse, Voluma), Sculptra, lasers, peels, and microneedling/prp. Implants or fat are an alternative. I recommend getting a formal evaluation with a cosmetic dermatologist. Chemical peels will not help volume changes or malar bags.  Best, Dr. Emer