What are these bulges/circles near the corners of my mouth and what can I do to get rid of them? (Photos)

This is likely an aspect of the buccal fat pad and possibly some dermal hypertrophy. A good physical exam is needed to determine which is contributing most to your dissatisfaction with the area. Buccal fat removal and manipulation can be a great and transformational procedure in the right patient.  Often times fat transfer in conjunction with this procedure is able to give a more “ideal” heart shaped face. This can make a significant difference in patients as a combo. It may seem counterintuitive to add fat when you say your problem is chubby cheeks. What we do is add fat around the cheeks to the side of the highest and most projected point of the cheek bone and taper it to the lower face. This helps to camouflage overly chubby cheeks.  This is especially helpful in thin women and in combination with buccal fat pad removal is a powerful maneuver. All of this can be done in clinic with some calming medications and local anesthesia.
I recommend getting a consult with a surgeon who does this procedure frequently to get a full facial analysis to make sure your specific goals are addressed.
Hope this helps.
Best of luck.
DrC

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 an in person consultation for a complete evaluation and explanation of the positives and negatives of this procedure in your situation. I hope this helps.