I have a small mouth and when resting my lips do not touch. Will getting a nose job help? (Photo)

I have a small mouth and when resting my lips do not touch. When they do, I have to force my bottom lip up which causes my chin to have a weird look to the middle. Will getting a nose job to make my nose longer and more curved at the tip help my lips to touch? Or should I get something done to my chin instead? I want to note I had braces for 3 years, when they got out I did not wear my retainer as I was supposed to so I got an overbite. Not sure if this contributes to my issue I am having now.