How to fix my downturned mouth? (photos)

The solution to the downward corners of your mouth requires attention to several areas on your face. From the pictures that you have posted you seem to have a very flat malar pad or cheek area. I would use a filler such as Voluma or Radiesse to round and lift it. In turn, it will provide better support for the lower part of the face and to the corners of your mouth. I also perform Botox injections to relax the depressor labii oris (DAOs) - the muscles that are normally pull the corners of out mouth downward. Fillers such as Restylane or Juvederm can be used in corners as well to open them up and upturn them. Combination treatments typically work the best.  Good luck

A rarely publicized procedure, the corner lip lift, works well for your situation .  It involves removing skin above the corners if the mouth.