What should someone do for undereye puffiness and for how long to treat it to get rid of it?

Try an ice pack like. Frozen peas(wrapped in a slightly wet towel ). Then i would guess you have a stuffy nose as well...Since the dark circles are due to the congestion pressing on the blood vessels under the eyes. Then try zyrtecd or allegrad( read labels for precautions etc) and see an allergist if you still suffer.