Asymmetric Smile - What to Do?

The 2 sides of the body are not the same and can never be made to be the same. Exact symmetry does not exist in nature. In your case even the bone sockets around each eye are not symmetric. You can make things a bit more symmetric though. My first suggestion would be a filler injection to the nasolabial folds as that is a quick relatively cheap fix with little downside.

There is no surgery indicated for correcting the smile muscles. To adjust the smile muscle, any type of surgery is done for static reasons and not dynamic reasons. A few drops of Botox placed in the right position may help weaken the strong side of the smile muscle and balance with the weaker side. Look for a dermatologist or facial plastic surgeon that has performed this many times. This Botox will have to be repeated every four to six months to keep up the results.  

Your facial asymmetry by photo looks relatively within normal limits. I probably would not recommend anything. If the lip volume is something that bothers you, then this can be balanced with some filler.