What are my best options to fix the deep lines in the corner of my mouth?

Thanks for the photo. Fillers continue to evolve, both in product choice and techniques to deliver them. I have had good success with a new Juvederm product called Volux to treat challenging marionnettes, chins and jawlines that previously did not respond adequately to other hyaluronic acid fillers. There is a considerable period of time following treatment with Volux of swelling and stiffness while the product settles into place, but the end result is a definite improvement over previous treatment results. Seek out a provider who has been using Volux for at least 6 months as your case is challenging. Best, Dr. Tkatch

Hello there,
       A lower face and neck lift is ideal to address your concerns. That being said, there are other options. I know you said you have tried different things, but I usually will do a combination of treatments to give the best result. 
     I will typically address the mid-face/lateral cheek area with filler to lift the tissue. I then would tighten the tissue itself with either Exilis Ultra or Ultherapy. Lastly, to address any volume loss/shadowing leftover, I would address the actual marionette line/jawline/jowl with filler. Hope this helps.
Sarah RN BSN