Puffiness after Cheek Lift and Lower Eyelid Blepharoplasty
The most likely explanation is that there is still some prominence of the lateral fat pad of the lower eyelid. Follow up with your surgeon so they can evaluate your situation.
Bag and puffiness under eyelid after having eyelid surgery
It is most likely that making a small incision in this region and "debulking" the tissue would be beneficial. As far as the fluctuating swelling goes, this is something that is unlikely to resolve with surgery alone.
If this turns our to be related only to swelling, then injecting the region with hyaluronidase may also be useful.
An in-person examination would be necessary to determine the cause of your under-eye puffiness.
This could be a prominent lateral orbital fat pad, or redundant skin, or fluid retention, or a combination of these. Best to consult your surgeon or another reputable facial plastic surgeon for an evaluation.
Hope this helps you.
Lateral lower lid fullness
could result from your prior procedure or could reflect excess fat around your eye ball. You need to see a surgeon (preferably your previous surgeon) to be evaluated for what it is then a plan to address it could be made and you can decide if you want to do it or not.