If you're dealing with burns or scars from chemical peel treatments, I would suggest speaking to the dermatologist or doctor you visited to receive these treatments. They will likely suggest a prescription cream or gel to heal this area, or they may consider TCA treatments, which can help with discoloration.
Other solutions your doctor may inform you about include steroid creams, steroid injections, or laser treatments to deal with the negative burn/scar effects from your previous chemical peel.
Lastly, you may ask about balms, mederma, and silicone sheeting to handle this issue.
Healing of the skin can take several months. For many chemical peels, people take a few weeks off of work to treat their skin. I have heard of discoloration lasting for up to a year, but burns and red marks typically go away within a few months. If you are concerned, I would visit the doctor you previously visited to go over treatment options and prices.