Ninety-nine percent of the time when I have a patient complaining of a new red mole, it is actually not a mole. It is a hemangioma.
Hemangiomas are a proliferation of blood vessels that start sticking out of the body. They present as bright, red, small papules that can happen on the chest, arms, or on the face. Oftentimes, they can happen after pregnancy or later in life. They are not moles in the sense that they are not formed by melanocytes, and they are not cancerous. The treatment is completely cosmetic, and they do not require a biopsy.
One percent of the time, though, a red mole may mean a skin cancer, specifically amelanotic melanoma. Amelanotic melanoma means the melanocytes have changed so drastically that they stopped making any type of pigment, and therefore they appear red to the naked eye. This is a very dangerous type of melanoma that needs to be diagnosed and treated by a dermatologist.
So if you have a red spot that is solitary, you do not have anything else like it on your body, it is important to see a dermatologist to make sure it is not amelanotic melanoma.