It is a bit difficult to analyze your mouth/lips without seeing more of your face. I suspect that you might have a relatively small lower jaw that leads to your lower lip drooping down a bit. Sometimes a lip reduction can be helpful. However, again you should have a complete facial analysis done by a qualified surgeon and they can provide the proper direction for you.
While it is difficult to evaluate your situation based on the available photos, it is true that some people have a "sadder" appearance around the mouth due to soft tissue factors, skeletal factors, and perhaps resting muscular tone. While there are actually fairly minor procedures that can give the appearance of a "happier" mouth, they are not commonly performed as the patient can be left with visible, although minimal scars. You really should have an evaluation with a facial plastic specialist who can more adequately evaluate you in person.