What procedures would fill in a labiomental fold?

Thank you for posting photos. There are several good ways to improve this crease. Injectable fillers are relatively easy and safe, but are temporary. Even the longer lasting fillers are not going to last more than a year or two. Surgery can address the soft tissues and/or the bones, is more invasive and risky, a lot more expensive, but the results are long lasting. If the skeletal evaluation reveals an underdeveloped chin bone or a jaw alignment problem, then orthognathic surgery is the way to correct it. Surgical soft tissue grafting with your own skin and/or fat is another option to fill in deep creases. Consult with one or more board certified plastic surgeons experienced in this area so you can be directly examined, then you can decide on the option you that you prefer. Best wishes!

Building up your chin underneath the fold with a filler like Sculptra or Voluma and then topping it with something softer, such as Juvederm or Volbella will give you the most natural look and feel. Evening out a labiomental fold takes a great deal of experience and skill so be sure to consult with a board-certified dermatologist who has expertise in this area. 

Thank you for your question. I suggest that you move forward and consult with a board certified facial plastic surgeon about your candidacy for lip enhancement. There are options available to create a natural looking result with a speedy recovery time. 
Best wishes,