Woke up with one eyelid swollen and under both eyes has puffiness. Under eye puffy is worse in the eye that the lid is swollen in?

Possible stye. Styes are common and usually imply less than perfect eyelid hygiene. Hot compresses are the single best treatment initially along with vigorous lid cleaning using warm water and terry washcloth. Compresses should be as hot as tolerable and at least 3-4x/day. If your eye is also red and draining you may have conjunctivitis; need a topical antibiotic drop. See your Eye Doctor if not better 48hrs.