What surgery would be best if I wanted to fix my upper lip from overlapping my bottom lip and for a fuller look?

Options for changing the appearance of the lips include filler injections, lip lifts, and others. The best choice depends on the patient's anatomy and the patient's desires/goals. An in-person consultation with a facial plastic surgeon who can review all of the surgical and non-surgical options with you in detail would be very helpful.
All the best,

Hello and thank you for your question.  Photos would be a great help in better assessing the issue at hand.  There could be many reasons for disproportionate lips (i.e. bone structure, dental anatomy, tissue anatomy, etc.) and therefore, it is best to have a specialist give you an in-person consultation. Fillers can usually achieve a symmetric look with little downtime and can be more cost-effective than having surgery.  Make sure to seek the advice of an experienced injector.  Best of luck!

Mia. photos would help but sounds like I may recommend conservative lip augmentation with Hyaluronic Acid, like Juvederm Ultra plus to see if you like the look. Another option is fat transfer which is more permanent. It is done under local anesthesia and fat is usually taken from the lower abdomen or thighs. Studies show that at least 1/3 of transferred fat last forever. Seek out a board certified plastic surgeon in your area, Good Luck!