What can I do to improve the aesthetics of my lips?

I think your lips are fine. You may want to consider volume augmentation, but if you do, I would be extremely conservative, putting fillers in your upper lip.
Midline asymmetry is usually more related to the asymmetry of the rest of your face.
All people have facial symmetry and it’s primarily based on bone structure.
During embryological development, the two sides of the face develop independently from each other and eventually fuse in the midline.
Most people have significant amounts of facial symmetry.
The human brain is accustomed to seeing facial asymmetry as being normal.
For that reason seeing a computer generated, perfectly symmetrical face creates an impression of seeing an odd face that is unfamiliar and strange looking. It also means that we don’t recognize people with a symmetry as having a symmetrical faces since it’s normal, and present on all people.
You probably don’t think of friends and family as having a symmetrical faces but when you notice it on yourself, all of a sudden it appears abnormal. If you look closely at any other person, you’ll see that all people have significant facial asymmetry.
Often the left eye socket will sit slightly higher in this goal than the right side. The left breast sits higher on the chest wall than the right side. This is true for both men and women. There are variations of this, but regardless the face and body are highly asymmetrical.
My personal best recommendation is to not have any treatment at all.
Best,
Mats Hagstrom, MD