My bottom lip sticks out compared to my upper lip. It looks swollen and is very uneven? (photo)

It is normal for the lower lip to be slightly fuller than the upper lip. As for the asymmetry that you mention, it is difficult to assess by the picture that you included. The shadowing distorts the way your lower lip looks. Still, lip reduction procedures are fairly easy to perform and can be done in an office setting under local anesthesia. The incisions are located on the inside of the lip. Any asymmetry could also be addressed during the lip reduction procedure.

Your lower lip can be reduced removing more from your right side to get the lower lip as symmetrical as possible. The scar would be inside the mouth. It is a short operations, but lips can swell.

a surgical reduction of your lower lip might work to improve your appearance. A scar would be present along the wet line of your llower lip which would not ne noticed by others