What Treatment Do You Suggest for Puffiness Under Eye and Top of Cheek?

The goal of surgery should be to move the fat lower to the level of your cheeks (if possible) to blend the eyelid into the cheek area. This approach is blepharoplasty with fat transposition. See an oculoplastic surgeon who is comfortable with this technique. 

It's not unusual for patients to request treatment of fat collections in the periorbital regions. Fat collections in this area can occur for a variety of reasons and the treatment will depend upon their causation.Unfortunately, without pictures or a physical examination, it's impossible to define your anatomic deformity and it's cause. Depending upon the deformity, a variety of treatment options may be available. These may include standard blepharoplasty, blepharoplasty with fat transposition, injectable fillers, midface lifts and lateral cheek lifts.For these reasons, it's important that your lower lid puffiness be evaluated by a board certified plastic surgeon with experience in this area. This surgeon should be able to formulate a treatment plan that addresses your anatomic findings and achieves your aesthetic goals.

Puffiness under the eye is much easier to correct than malar crescents or festoons, which occur at the top of the cheek.
If you are a smoker this can contribute to the formation of these swellings, and surgery will not help unless you quit smoking.
There are different causes for these to develop - some are muscle descent, and all approaches to their correction are limited by persistent swelling after the surgery.

The puffiness under the eyes is traditionally taken care of with a lower blepharoplasty through a transconjunctival approach on the inside of the lower lid. If the tops of the cheeks are very flat, consideration for cheek implant augmentation should be done. It is important to have a smooth transition between the lower eyelids and skin of cheek for a youthful appearance.

This area has always been a difficult one to address surgically, which is the reason for the numerous types of cheek and mid-face lifts, some of which are fraught with complications, especially in the hands of inexperienced or naive surgeons. Thankfully, the options for malar pads and the lid-cheek junction continue to expand and include fillers, laser liposuction (acculift with the accusculpt laser) and surgery. Which one might be best for you is best dtermined with a face to face consult and discussion of your goals with an experienced surgeon.