Mounds of flesh around mouth and uneven jaw - what treatments are available to correct this? (photos)

Thank you for your question. Lip procedures can correct your mouth to create a smooth and supple lip area.  I suggest that you move forward and consult with a board certified facial plastic surgeon to develop a treatment plan because it sounds like you are also interested in improving your jawline and chin areas.
Best wishes,

The mounds by the side of your mouth to which your refer are known as perioral mounds. These small subcutaneous collections of fat can be removed by small cannula liposuction from an incision inside the corners of your mouth.

Hello and thanks for posting.
One of the approaches to address this issue and create a smooth and supple appearance of your lower face and lip region is to use facial fillers. Facial fillers can be used to feather in the subcutaneous region around your prominent modiolus. You can also have fillers to better define your jawline as part of a holistic approach to facial reshaping.

I hope that this information helps and best of luck to you!