Lip Incompetence and Mentalis Strain- Easiest Way to Fix? (photo)

I can't close my lips at rest. I have to consciously push them together, and when I do, I get mentalis strain. I had braces years ago and my bite is perfect, so I wouldn't want to undergo jaw surgery. Is botox a good idea for the mentalis strain? Or would Botox weaken my muscle so that I couldn't close my lips properly anyway? I was hoping Botox could be administered to stop the chin strain, allowing me to close my lips without strain. I attached a frontal and side pictures of the problem