Hi
Welcome to the forum!
Well, as Surgimenopause said drooping of mouth to one side can be due to Bell’s Palsy, which is actually a self limiting disorder managed conservatively by medicines and exercises.
It could also be a stroke causing dysfunction of the facial nerve. Other possibilities are dental caries or infection of the mouth on one side that is making the muscles of that side go into spasm. Hence that side appears to droop on smiling.
Discuss these possibilities with your doctor. A comprehensive investigation is required keeping all the points in mind.
Hope this helps. Please let me know if there is any thing else and do keep me posted. Take care!
If the doctors have already eliminated a stroke, try looking up Bell's Palsey. I relative of mine had this. I found that she should massage it frequently I think online. She did and her smile came back after awhile on the side where it had drooped!