Asymmetric Peri-oral Mounds
I would recommend not trying to alter these mounds but instead I would blend surrounding structures to help camouflage the mounds. Therefore,subtle filling above,below,and lateral to the mound will help to diminish the appearance of the mounds.
Very small cannula microliposuction done from small incisions inside the mouth is the definite treatment for these small fat collections by the sides of the mouth.
How to correct the mounds around the sides of my mouth, which are much more prominent on my left side.
You are a beautiful young 28 yo woman. There is nothing that i would offer you at this point because what you are noticing and highlighting is not something that is a big prominent part of your face. Your lips are nice and full and have a nice shape to them. Although you notice this, it is not something that readily jumps out. For this reason I would tell you to not chase this. You have other beautiful attractive features on your face that you should focus on. Good luck
Volumizing Fillers Work Well To Treat Early Jowl Formation
From the photos, it appears that you are demonstrating early sagging and jowl formation in the region around the mouth. A close examination shows some volume loss at the lower poles of the cheeks, which appears to be contributing in large measure to the problem.
A bit of volume repletion in that area is likely to give sufficient lift to the area immediately below around the mouth to straighten the angles of the mouth and mitigate or entirely eliminate the incipient jowls. If not, the addition of a small amount of volumizer injected immediately below and within the mouth angles themselves would likely do so. In my Upper East Side Manhattan practice, I would opt for Restylane Lyft for these purposes. (In my Israel satellite facility, where a far greater number of regulatory agency approved volumizing fillers are available, I would opt for Hyaluronica 2.)
You would be advised to seek consultation with a board certified aesthetic physician.
"Mounds" that need treatment
You are having the very beginning of facial aging with a loss of skin laxity and sagging. A combination of fillers to lift the mid-face area and Thermage to tighten the skin would be the best combination to treat you. Best, Dr. Green
Weight loss effects face too
From the pictures you are showing, it looks like you have drooping on the sides of your mouth due to diminished cheek volume, from weight loss. This is easily fixed with Voluma. I recommend you see a Board Certified Dermatologist or Plastic Surgeon who is skilled with injections and fillers.
Lumps in corners of mouth
This are may be fatty tissue or muscle. If it is fat, it might be favorably treated with liposuction. Best to be seen in person.
Hard to say for sure without physical exam but your lips appear fine to me, attractive and full. The fullness you describe just lateral to the corners of your mouth may be well defined areas of fat, highly amenable to micro-liposuction. Be sure to consult with a board certified plastic surgeon. Good luck!