Do Receding Cheekbones Make Eyes Appear Puffy?

Though small cheekbones can make the bags in the eyes look bigger, the usual cause in someone as young as you are has nothing to do with aging. Allergies with puffy lids can be seen in 10 year old children and only go away with surgery or total avoidance of the allergen.

The eyeball sits in a bone walled socket & is cushioned by surrounding fat. This prevents the eyeball from sustaining damage by striking the bone side walls.
The lower eyelid has a 3 layer construction:
1-the outermost layer consists of skin & eye closing muscle
2-the middle layer consists of cartilage, eyelid lowering muscle & a thin membrane that extends between the cartilage & the outer lower bone edge of the eye socket
3-the innermost layer consists of the conjuctiva a membrane like tissue that produces tears & covers the eyeball when the eye is closed

As one ages the membrane in layer 2 between cartilage & eye socket rim stretches. This membrane normally holds the fat that surrounds & cushions the eyeball in place within the eye socket. However, once it is stretched out it can no longer keep fat within the socket. This protruding fat then gives the appearance of puffy eyes or lower eyelid bags. The puffiness can be exagerrated by the connection between membrane & eye socket rim. This connection creates a sharp margin between cheek & eyelid skin exagerrating the puffy look.

In the examination before any lower eyelid surgery I look at the plane that connects the outer edge of the cornea with the cheek bone under the eye from a side view. When this line or plane is angled downward to the back the cheekbones are positioned further back and we call that a negative vector. When the line or plane is directly vertical it is a neutral vector. When it is angled forward the cheeks bones are more prominent and we have a positive vector. Negative vector patients are more susceptible to complications after lower eyelid surgery (ectropion) and undergo aging changes of the lower eyelids earlier in life. I am not sure if it has been adequately proven that this is reversed by placing cheek implants.

As we age, our entire face changes.  Not only does the fat in our face change and drop, but also there are decreases in bone mass as well.  Puffiness under the eyes is largely due to herniation of fat under the eyes, along with changes in the skin and connective tissue.  However, as the fat and and bone of cheeks decreases also, it may actually make the puffy eyes look more pronounced. 

There are several ways to correct undereye puffiness.  In some cases, by building up the cheek with a filler, you can mask the appearance of the puffiness without actually treating it.  In other cases, a surgical correction of the eyelids is necessary.  It is important to get an evaluation by your dermatologist or plastic surgeon to go over your options.