What are these fat pockets around my mouth and can they be removed? (photos)

Thank you for submitting your question and photos. I
would not recommend liposuction to the face. The risks outweigh the
benefit. A consultation with a Board certified Plastic Surgeon will give you the best plan. Best wishes

A modest amount of fat grafting to the submalar area just lateral to the nasolabial line will improve this.  It is relatively straightforward procedure that can be performed under local in the office. 

Always best to have in person examinations vs over the internet guesses. But my guess is the cause is genetic aging and weight loss. Recommendations: off label low dose KyBells injections and/or Silhouette mid face Lift with Dr B's 1 stitch facelift options and/or ThermiTight RF to Smooth RF therapy. .