Yes, smoking will cause your puffy eyes because of the stimulation from the cigarettes. Your eyes nerves are affected which cause the puffy eyes. You'd better stop smoking and use the warm compress to make the eyes feel comfortable. You could also use the eyes drops to make the eyes become moisture. You could have a try.
All right, I know that you are annoyed by those puffy eyes, or eye bags, and those things would make you look bad and have less confidence. Anyway, puffy eyes could be resulted from a lot of factors, so you must take anything into consideration if you want to change the situation. Generally speaking, aging is the main factor, but smoking do harm your skin conditions. So you must try to quit some bad habits and maybe try some cosmetics such as retin A.