What can I do about one side of my face being fuller?

Most patients have a mild facial asymmetry in which one side of the face is slightly smaller or larger than the other side. In some cases, the difference could be noticeable to the point it bothers the person. In these cases, some plastic surgery procedures could be performed to achieve a more symmetric face.
Asymmetric buccal fat removal  (either removing more buccal fat from one side or removing fat from only one side) could help to achieve more symmetry of the LOWER anterior face.
Asymmetric cheek enhancement (placing more filler in one side cheek bone) could help to achieve a more symmetric UPPER face. 
Patients interested in asymmetric face improvement should make a consultation with a board certified plastic surgeon specialist in procedures of the face like buccal fat removal and fillers.

There are a variety of techniques that can be used to correct facial asymmetry. A more temporary approach includes dermal fillers (e.g., Sculptra, Voluma, and Radiesse), while fat grafting, use of permanent fillers (Aquamid, Bellafill ) and facial implants would offer a more permanent solution. To address your concerns I would recommend having an in person consult with a board certified plastic surgeon who specializes in facial aesthetics.

Buccal fat excision is an appropriate surgical procedure for patients that of overly full and wide cheek areas. In common terms, it is good for patients who have chipmunk cheeks. In reviewing your pictures, is difficult to tell if you're a good candidate because your cheek area is slightly full but not overly full. You are a patient that would need and in person consultation for a complete evaluation and explanation of the positives and negatives of this procedure in your situation.
I hope this helps.

Dear BirdIsTheWord,dermal fillers are a great option to resolve face asymmetry. If you are considering any procedure, I would suggest you to consult a board-certified plastic surgeon. Only after a thorough examination you will get more information and recommendations.Daniel Barrett, MD, MHA, MS 
Certified, American Board of Plastic Surgery  
Member, Am. Society of Plastic Surgery

Thanks for your question

The buccal fat pad is a rounded mass of fat in the middle of your cheek. It’s located between facial muscles, in the hollow area beneath your cheekbone.
The size of your buccal fat pads affects your face shape. Everyone has buccal fat pads. However, the size of buccal fat pads can vary greatly. If you have larger buccal fat pads, you might feel like your face is too round or full. You can be a candidate for a Buccal Pad removal surgery.

Best of Luck