Why does my bottom lip goes to the left side when i smile? (Photo)

Thank you for your question and the photo.  Yes, I agree. Your depressor anguli oris is weak on the affected side.  Did you have previous oral or head and neck surgery or some other type of trauma?Yes, small doses of Botox Cosmetic on the opposite side can give some improvement.See two or more board certified physicians in your area for a complete evaluation.I hope this helps.

You have weakness of your DAO muscle on your right side.  There may be an injury to a branch of your facial nerve that controls this muscle.  Have you had any prior head and neck surgery, trauma, or Bell's palsy?  If the asymmetry of your smile bothers you, it can easily be improved by treating the left side with a little Botox.   

The depressor of the right angle of your mouth (muscle) is not working.  The lack of function might be related to past trauma. Nothing can be done to get it back to work.   Your left one is overcompensating creating a left maximal pull on the lower part of the left side of your mouth. However, the left side can be inactivated with Botox  or other botulism toxin for temporary banlanced smile.   

From the picture, it appears that you have a weakness of the muscles that pull your lower lip down and this results in the crocked smile that you have.  There can be many reasons for this but usually it is the result of an injury at some point to the nerve that makes those muscles work.  Unfortunately, there is very little that can be done to correct this.  Some people will try Botox on the other side to see if you can get a little better balance.I hope that helps.  Best regards.