What is the best treatment for lower face when “pockets” start on sides of mouth? (Photo)

It appears as though you could do one (or more) of 3 things to help lift the pockets that are forming on the sides of your mouth.  This is also referred to as jowling or descent of the cheek fat pads.  You could do:
1.  Facelift - this is an great way to lift the jowls and rejuvenate the neck and jawline as well.  The results typically last 5-10 years.  The surgery takes about 4 hours with about a week of downtime.
2.  Fillers - Restylane Lyft or Juvederm Ultra are good fillers to camouflage the jowls by filling in the areas around them.  They can also be used as a sort of lift underneath the jowls.  The procedure takes about 30 minutes, but the results only last for about 6 months.
3.  CO2 laser - this laser is great for helping to remove fine lines and wrinkles from the face.  You also see some skin tightening with this laser treatment.  The results last about 1-2 years, but it does involve sedation in the OR with about 1-2 weeks of redness and peeling from the laser.
Moreover, it appears as though a facelift would be you best option.  Pain is minimal and again recovery takes about a week of staying out of the public due to bruising and swelling.
Thank you for your question!
Dr. Schreiber, Baltimore plastic surgeon

Picking the right procedure for facial rejeuvenation involves expertise in the different procedures. I would need to examine your face and hear what bothers you and determine if I can help you achieve your goals. The Vectra 3 dimensional imaging machine can help us discuss what can and cannot be achieved. See a board certified ASAPS plastic surgeon in consultation. Good luck...