Is There Anything I Can Do to Fix my Crooked Smile?

I agree with both Dr's Aldea's and Rand's statements. Your face is asymmetric and you could achieve better symmetry by relaxing the upper lip muscles on the right side of your face. Prior to doing so, however, you should determine if you prefer symmetry with decreased upper lip movement on both sides of your upper lip. Essentially this treatment will lower your normally active right side because there are no treatments that can restore or increase activity of the muscles on the left side of the upper lip where the problem really exists.

The asymmetry with smiling is due a nerve injury weakening the muscles that elevate the lip on the injured side. To correct this, Botox can be  injected into the "stronger" side so that it can "match" the weakened side. Botox in the lower face is an "advanced technique" so find a physician that is familiar with all the facial muscles, such as a Plastic Surgeon.