Sometimes when my toddler has a cold or is sleep deprived he gets what looks like a black eye under one of his eyes. What is it and should I be concerned? He does not seem bothered by it, but it just looks awful.

Blood vessels . The tiny blood vessels under your eye can become congested during an infection or from lack of sleep. The thin skin under the eyes reveals the blood vessels below the skin and causes the area to have a dark or bruised appearance.
SHINERS. Darkness under the eye is cause by congestion which cause the blood flood to be sluggish. This causes the darkness under the eyes. They are called allergic shiners because it is seen in many kids with allergy but it is not only seen with allergy.