Fat Pocket Above Cheeks? Lower Eyelid Problem? (photo)

Puffiness under the eyes can be caused by many things (multifactorial).  I agree with you - it looks like your area of concern is malar edema/festoons (swelling) rather than classic lower eyelid fat pads/bags. 
Malar edema can be caused by a number of issues including genetics, aging, fluid retention, salt retention, lifestyle, alcohol, allergies, sleep, and unknown reasons.  Without a doubt, malar edema is a difficult problem.  Traditional lower eyelid lifts (blepharoplasty) do not fully correct malar edema and can make it worse.  Injections with kenalog (steroid) or 5-FU and taping may help but I have not seen them completely treat this area.  Fillers can sometimes blend and camouflage the area but this treatment is variable.  Direct excision of the festoon is the best definitive treatment but you are trading the puffiness for a scar.  Usually that is reserved for more prominent festoons.  The scar can be camouflaged, thin, and the pinkness will fade.  You have to consider how much the area bothers you and discuss this with your surgeon.    
I would consider a consultation with your primary care doctor to evaluate any underlying conditions that can cause salt retention or fluid retention.  If you have bad allergies, you may be a candidate for allergy treatments beyond an antihistamine.  I also recommend a consultation with a qualified surgeon for an exam to discuss your options. 

These appear to be festoons and are very difficult to treat.  Make sure your allergies are under control with antihistamines, cortisone nasal sprays, allergy testing, etc.  Fractioned laser would be of some benefit to try to reduce the interstitial fluid retention inside them.  A blepharoplasty will be of no benefit