Fatty "pockets" around corners of lips? Is this something that can be changed?

tigolbittiess.   It appears from your photographs that the areas demonstrated may be part of something called Buccal Fat pads. These may be able to be trimmed through small incisions inside the mouth or possibly removed with micro-Liposuction. Physical examination is needed to for certain diagnosis. Be certain to consult a board-certified plastic surgeon. Good luck

Thank you for your question and pictures. You can have excellent improvement with what I like to call microsuction. This is liposuction done with a very thin cannula. The incisions are at the corner of your mouth, so they are not visible. This can be done under local anesthesia.

The fatty "pockets" around the corners of your lips can be addressed through a few options. These areas may be due to localized fat or tissue laxity. Dermal fillers, like hyaluronic acid, can smooth out the region and create a more balanced look. For a more permanent solution, liposuction or minor surgical contouring can remove excess fat. If sagging skin is also a concern, skin-tightening treatments or a small lift may be needed.
Consult with a board-certified plastic surgeon to explore the best approach for your needs and desired results.

The fullness to the sides of your mouth is known as perioral mounds. These are excessive collections of subcutaneous fat which can be removed though a microliposucion techniques from a small incision inside the corner of the mouth.