Puffiness in the lower eyelid is usually due to pseudohernias of fat which requires removal via transconjunctival or external blepharoplasty approaches, usually.
Puffiness in the cheek (and occasionally the lower eyelid) can be edema fluid and is referred to as malar pouching, festoons or crescents. This is graded as to severity and whether this is static or fluctuant in nature.
Treatment can include dilute deep steroid injections and massage, radiofrequency treatments (monopolar, bipolar, unipolar) direct excision, and extended transcutaneous lower blepharoplasty with cheek lifting, among other options.
However, this problem can be more difficult to treat than the eyelid, so you are forwarned. Consult an experienced eyelid surgeon.