Which procedure would minimize the appearance of my asymmetrical smile and double chin? (photos)

First, for double chin, we have many options. It doesn't show well in this photo, but, there are surgical options (neck lift) through a small incision under the chin, there are minimally invasive options (like liposuction, or necktite), and there are nonsurgical options (like fat freezing or kybella). Some of these are better than others, and a video call will help us sort what's best for you.

For your smile, again, this photo isn't the best view, but we can consider tissue augmentation, partial lip lift, or even filler injections. The good news is you have several options.

There is not enough informtion is a single picture but it looks like you have an undereveloped maxilla that is not supporting your facial tissues.
Maxillary development will better support your lips and decrease or eliminate deep nasolabial grooves.
This will also improve your airway and forward head posture