How can I get rid of the puffy and dark areas around my eye from allergies?

Cool, elevation, ... The dark areas come from dilated vessels just beneath the skin. When your eyes are irritated, these vessels become more visible. Also, the skin is a bit water-logged & thus sometimes more transparent. The puffy part is best helped with elevation (extra pillows for sleep) and cool compresses. Save teabags for drinking. Anti-allergy oral & topical meds help too.