Chemical peels are not advised for facial skin since the skin on the face is sensitive as compared to the rest of the body and runs the risk of reactions. To improve facial complexion it is advised to use a sunblock (SPF 30 and above) when exposed to the sun. You could also try creams/ ointments containing tretinoin, hydroquinone, arbutin, azelaic acid, niacinamid etc. It is advisable to use these at night. If these do not seem to help, you may consider seeing a dermatologist for alternative management.
Hope this is helpful.