Clogged pores, acne, or skin discoloration can occasionally result from having oily skin and an oily nose. Pigmentation, allergies, irritating the skin, sun exposure, sleep deprivation, or irritation from cosmetics or creams can all cause an unexpected black area under the eyes. Use sunscreen, prevent severe scrubbing, wash your face twice a day with a moderate face wash, and avoid applying steroid or random fairness creams. See a dermatologist for an appropriate assessment and treatment if the dark spot is growing, itchy, painful, or changing in shape.