Alcohol can definitely contribute to under eye puffiness. It could also be from lack of sleep and dehydration. Make sure you are getting your beauty sleep, avoid alcohol and drink lots of water.
Puffiness could be caused by sinuses. It could be caused by edema, your body just hold fluid. And sometimes maybe you sleep too hard to where your eyes just get puffy and swells.
Alcohol can cause it. So can lack of sleep and dehydration(and a combination of all after a late night out on the town). It also can be cause by crying or sickness.
Puffiness under the eyes is fluid retention. Sleeping on your stomach, alcohal and anything else that keeps you from getting a good night's sleep can cause eye puffiness.