Can aphids live under the skin?

No, aphids can't live under the skin. They're outdoor insects that like to eat plants. It's possible for parasites to live inside of a living body. But there's nothing inside a non plant body that has anything to offer an aphid. An aphid would starve and wouldn't survive.

That aphids can enter and thrive in human bodies is a misconception from the 2006 film 'Bug'. The character that Michael Corbett Shannon [b. August 7, 1974] plays believes that aphids can enter and take over human bodies. His belief is an indication of his mental state and not at all a reflection of reality.