My skin under eye is purpleish and my eye hurts when i blink what is going on?

Difficult to say: Without a picture it is really hard to say. I'm not sure if you are describing an early bruise around the eye. Was there a history of trauma? I really would see your local eye md for a specific answer as it will likely warrant a good examination. Good luck!

Clogged oil gland: Possibly a sty. A sty is when an oil gland of the eyelid margin gets clogged and the oil backs up and forming a pocket of stagnant oil and the eyelid becomes inflamed. A hordeolum is the acute phase or beginning stage of a stye, and a chalazion is the chronic phase (where the oil becomes more granular, thick and the skin inflammation resolves, but there is still a bump/nodule in the eyelid).