Thank you for sharing your question and photographs. It appears that your piercing resulted in the development of scar tissue to your right lower lip causing the volume asymmetry. I would recommend a procedure to reduce the scar tissue to achieve a more uniform and soft lip appearance. I hope this helps.
You probably developed scar tissue after the piercing. Sometimes a small reduction is beneficial....
It sounds like you may have some scar tissue causing your asymmetry. This could probably be reduced in the clinic under local anesthesia.
I appreciate your concern. Your best option is a conservative lip reduction reducing the larger side. The surgery can be done in the office under local anesthesia. Check out the link below to an article I wrote about the subject, it may be helpful. Be sure to consult with a board certified plastic surgeon. Good luck!