I would like to know of any procedure that will help my upper lip overhang? (Photos)

This typically needs laser or small lip surgery to improve but sometimes fillers can be used to camoflage them.  See an expert.  Best, Dr. Emer.

A small local tissue rearrangement with or without mucosal excision will correct that minor issue.  Z-plasty of the frenulum, chevron shaped excision, V to Y plasty, W plasty, or vertical incision with horizontal closure will do it.  That's 30 minutes, local anesthesia, office procedure, absorbable sutures.  No fuss, no muss, no bother.

Thank you for sharing you question and photographs. It appears that you have some mild excess internal lip mucousa which can likely be treated with a small reduction surgery.  See an ASPS board certified plastic surgeon in consultation to discuss. 

peannutbutter   I appreciate your concern and while physical exam is optimal, your photos demonstrate that you would most likely benefit from lip reduction surgery. The procedure is done in the office, under local anesthesia, and it takes about one hour. Recovery is usually one week, as postop, the lips are quite swollen. Be sure to consult with a board certified plastic surgeon. Good luck!

That area can be revised in the office under local anesthesia. I would suggest meeting with a board certified plastic surgeon and discussing your options.

Hello and thank your for your question and good pictures! Rather than injectables alone, I would think that this will involve a surgical reduction procedure to treat the inner lip that seems to have some mild excess. As this is a specialty surgery I would strongly advise seeking consult with a facial plastic surgeon.
Best Wishes,
Mr Golchin

Peanutbutter,
Thank you for the pictures. It looks as if you have mucosa (tissue lining the inside of the top lip) that hangs down when you smile wide. This can happen if you have excess mucosa or a tight / long frenulum. The upper labial frenulum is the fold you can feel with your tongue attaching the inside of your lip to the upper teeth gingiva. A tight or elongated frenulum would push mucosa from the inside of the upper lip down when smiling wide. An evaluation with an experienced and trusted aesthetic surgeon is recommended to evaluate the appropriate care. Option could involve reducing the frenulum, mucosal reduction surgery, and microdroplet steroid injection into the mucosa, to name a few. 
Hope this helps!Hardik Doshi, M.D.