The person who examines your moles, acne, and other skin problems is called a dermatologist. Once visited mainly for acne problems, dermatologists have become more important, as skin problems have grown more common with our increased exposure to the sun.
You know that an "-logy" at the end of a word means "study" and that "-logist" means "one who studies. In the noun dermatologist, the object being studied is the derma, the Greek word for "skin." (The Greeks also used it to refer to "leather" or "hide," which still works for diehard sun worshipers. And think of elephants being called "pachyderms," with their "thick skin.") Dermatology and dermatologist both appeared in English in the 19th century.