Puffiness under the eyes or more commonly termed as eye bags may be due to the decrease in elasticity of skin as one ages. The skin beneath the eyes are quite fragile or rather delicate. They are also not as tense and as elastic as the skin in other parts of the body.
I would not advise that you apply OTC creams over the area as this may cause darkening or discolorations of the skin .They may also aggravate the puffiness. Cosmetic surgery may be of help but is expensive. For natural remedies, cucumber slices applied over the eyes may cool and soothe the eyes. Drinking plenty of water, applying sunscreen with an SPF of at least 30 on the face