Chemical Peel with Thin Skin (Age 60)

I have had many blistering sunburns as a young adult. Some were so severe my forehead retained fluid. I have very fair skin and at age 60 very thin skin. I have had numerous spots frozen on my face, hands and arms but they continue to erupt and the doctor is recommending a chemical peel. I am concerned about my thin skin and wonder what procedure would be best. I am not concerned about my wrinkles as much as skin cancer.