What is this shadowing on the right side of my mouth (left in photo) & what can I do to fix it? (Photos)

Thank you for the photos. One of the possibilities is that you are holding tension in your lower face when you are smiling, hence you are creating a wrinkle subconsciously , which shows up as a shadow on photos. The solution is expertly placed botox to chin/underchin area.You can also have a little lip filler. As long as you discuss with your provider that you wish for a subtle look, they should choose a soft filler like Juvederm Volbella or Restylane silk. You may even try a little botox lip flip, but it generally lasts 1-2 months and may affect your ability to purse lips or to drink from a straw. Some patients don't mind it, while others hate it. It's a journey. You should try different options to see which one would work best for you and make you feel the best.
Best, Dr.Anna Avaliani, NYC

I think filler (such as Kysse, Volbella, or off-label Vollure) in the upper lip would do nicely. As long as your provider understands that you want a subtle look, then they will use less filler and it will look very natural. I have many patients who prefer subtle, natural lips and they love that people would never guess that they had lip filler.
The shadow along the right side of the lower lip is due to the muscles of the face showing. It is reasonable to do a thin filler (such as Volbella, RH redensity, or Belotero) to smooth out the surface. Skinvive, which does not volumize, but does hydrate is another option. It may help to show the photos to the injecting provider, so they understand your concern. These are nice options because you can dissolve them if you do not like the result (with injections of the enzyme hyaluronidase). Other options include platelet rich fibrin (such as EZ Gel), nanofat, or off-label exosomes. These help your cells heal themselves and have great results, but they usually cost more.