Why is my lower lip sticking out like this, especially when I am smiling? How can I fix it?

There are surgical and non-surgical approaches to lip augmentation. Non-surgical approaches include botox (slight lift, reducing gum show) and filler (volume restoration). Surgically, you can have two separate incisions under the nose (italian), one incision under the nose (bull horn), one incision at the red/white upper lip junction (gull wing) or two separate incision at the corners, or a combination, depending on your desired look and anatomy. My preferred surgical technique is called the Elelyft, which is a version of the bullhorn approach. 
In your situation, you should consult with a oral surgeon regarding the alignment of your teeth and if the jaw bones need to be adjusted. The chin is slightly under projected and augmenting it with filler or implant might take attention away from the lower lip. Only after these considerations would I advise further discussing a lip reduction. 
Consult with an experienced lip surgeon for a complete range of options that are appropriate for your situation.
Gary Linkov, MD
Lip Specialist / RealSelf Lip Lift Medical Reviewer
Manhattan

I appreciate your concern, however  physical examination is needed to confirm my advice. It appears that your lower lip is a bit larger,  compared to your upper, however it is not unattractive. Also you have a somewhat crooked smile, but I do not think that your lips are asymmetrical. I would strongly consider all options before undergoing a Lip Reduction surgery as your lips are attractive and I am not sure I would do anything if I were you. Good luck.