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

Based on your limited pictures, a combination approach would be best to consider. Replacing some lost volume with filler is an excellent option and doing something to tighten the skin at the same time, would be ideal. The natural aging process on the face involves both facial volume loss and loss of skin elasticity- majority of the facial treatment options address these conditions. Your filler options vary from injectables such as restylane, juvederm, voluma to facial fat transfer and your skin tightening options vary from nonsurgical to surgical depending on the extent of the laxity. This is an overview of your options and more can be explained at a consultation. 

These bulges right next to the corners of your mouth are pericommissure bulges and different than regular jowls. These can be very hard to treat. A facelift can definitely help in pulling them back and making them flat however, sometimes you need fillers to camouflage them as well. Start with simple stuff i.e., fillers and then proceed to surgery if not better. RegardsDr. J

Thanks for sharing.  It looks like some excess skin laxity has created this fullness outside the mouth. A lower facelift will allow this excess skin be tightened and smooth out this bulging area.  The buccal fat may also be contributing to this fullness and your surgeon would need to examine you to determine if this needs to be addressed.  

The bulging that you appreciate around the sides of your mouth is called Jowls and this is part of the normal aging process in all individuals.  Thinner women tend to have more prounced skin jowling but patients with fuller faces are also susceptible to jowling of skin and fat.  The proper solution depends on several factors.  One of which is your weight and the amount of facial fat that you present with.  The other variables will depend upon what your are willing to have done.  Less invasive procedures like filler injections will help.  Laser facial skin tightening will also help. Thread lifting can provide some impressive results in your case with minimal downtime and a well performed minimal incision facelift witill also be part of the conversation.  Combition treatmens using facial filler or fat injections along with some sort of lifting procedure will also look quite nice.

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... 

I am not a fan of fillers overall.  You would probably get better improvement with a facelift, depending on your age.  Expect partial improvement but I believe more worthwhile than fillers.

In order to evaluate accurately in person exam is essential, as well as all views of the face. If you have excess skin in the neck, jowls, cheek area (which it appears you have from a limited photo) - then you are a candidate for facelift/neck lift. In the right hands- patients can expect a very rejuvenating, long lasting result. I suggest that you seek an experienced Board Certified PS for in person exam

Your pockets by the side of your mouth appear to represent lax skin as evident by our very thin face with little subcutaneous fat. A limited lowe facelift, possible combined with submalar cheek implants, would provide the most assured removal of these pockets and to smooth out the skin from your mouth corners back to your ears.

Dear Elaina70, 
Thanks for sharing your photo. 

The beginnings of facial skin laxity start when skin repair diminishes and passive skin aging relaxes downward. The web of fibrous compartments under the skin loses fat, stretches and elongates developing 5 growing “waves” of skin at points of attachment such as the:

hooding along the eyes,
lower eyelid / cheek junction or tear trough / nasojugal fold
nasolabial fold,
lateral mouth commissure and marionette folds, (your "pockets")jowls and neck.
Facial Aging are created from the 5 different layers of the skin, fat, muscle and bone. During the first 20 years or so of life, the body genetically determines how to develop and repair a constantly changing “face” including all these layers (as it does elsewhere in the body). Thereafter it remains robust in repairing itself from injury but the accumulation of environmental, health and nutritional exposure will add to the passive inability for the body to care for itself after 30. This is when physical changes such as skin laxity, irregular pigmentation, lines and wrinkles and skin diseases occur. We now have many options to rejuvenate the layer or layers of the face which need care or stimulation to reverse the aging trend.
So, it is important to understand there are 2 layers of the face and neck to rejuvenate; the laxed visible skin AND the sagging soft tissues under the skin. 

Today's options offer non-invasive, minimally invasive and surgical options. In general:

The lower face can be reduced, lifted, tightened, and / or
The mid-face can be filled. 
Since I do not have the advantage to examine you, I hope you will be helped by the information below. My immediate recommendations are to obtain:

consultation with a talented, Board Certified Plastic Surgeon with extensive skills in:
non-surgical skin tightening using Obagi ZO Skin Health Rx regimen and chemical peels
minimally invasive injectables including fillers and / or fat to the mid-middle-lateral upper cheek
Minimally invasive EuroThreads of soft tissues and skin, ie 2 layers for firming and tightening of the dermal skin layerlifting of the jowl and marionette / lateral commissures / nasolabial foldslifting of the jowl directly upward back to the middle upper cheek.Everyone needs one or more layered improvement and in personalized combinations to achieve their optimal result. You can understand why it takes a talented individual, preferably a Board Certified Plastic Surgeon with great experience to evaluate your needs and find a plan that works best for you. All surgical, minimally invasive and non-invasive procedures and their combinations should be discussed following a proper examination with a well versed, Board Certified Plastic Surgeon who performs all of these options so you will not receive a biased approach because he limited in his skills.
I trust this is helpful. All the best!