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! 

yes your desires are entirely unrealistsic. You are young and  extremely attractive. The architecture of you lips are such that the corner of the mouth undercuts the soft tissue. The bulge that you see may be fat but also maybe contain a branch of the facial artery. I have tried to improve this by liposuction and found that it didn't work, Actually if it did work you would probably get a little crease where the fat was removed.  Trying to fill the corner of the mouth to elevate it to the level of the cheek will result in an ugly lump. The best looking people are the least secure about their looks........unfortunately people who are insecure about things  on their faces often get talked into doing things that make something that only you notice into something that everyone notices.