You have an issue with your bone structure not your lip. However, you can do upper lip filler and chin filler to help the look of your lip balance. If you want a more dramatic look, you need maxillofacial surgery. Best, Dr. Emer.
If you want more show to your lip you will need a lip lift. otherwise fillers can be used. botox around the mouth as well. I would use daily hydration and plumping (see emeragecosmetics.com lip essentials kit). everyone can do a little filler when done well really gives nice hydration and ...
This is my expertise and a huge portion of my practice. Asymmetry is normal and expected. See an expert who does facial shaping with surgical and non surgical methods to get a comprehensive option. Best, Dr. Emer.