You could have had the nerve that pulls down the corner of the mouth (the marginal mandibular nerve, a branch of the facial nerve) injured. I would discuss with your surgeon, but the best option would be to go to a facial nerve center, where there is a multi-disciplinary team that can address the issue. You can go to this site to find out more: healthcare.utah.edu/ent/facial-nerve-center.
Although pictures and an examination would be much more helpful, your description is suggestive of injury to a branch of the facial nerve (marginal mandibular branch). Marginal mandibular nerve injury is usually temporary, recovering within 6 weeks to one year. No improvement at 12 months is somewhat concerning and is best evaluatedby your operating Surgeon.
This is a classic problem that clearly bothers you and is a mystery. I do not know why you have what you have, I guess you could have had some nerve changes but bilateral is rare. You need to go back to your original surgeon and get an assessment. Then visit 2 other ABPS certified surgeons for more opinions. You might consider putting pictures of yourself on RealSelf so we can all clearly see what the problem actually is. Mystified at this point. My Best, Dr C