My daughter had warts, not sexually transmitted, on her hands. Her doctor used a basic, over-the-counter, wart freezing system. It was used one time on each wart, and they eventually fell off. I am not sure if I would recommend using it on the lips though. The hands would be okay though.
The treatment of wrats depends on the size and area involved. For small warts, several medications(like podophyllum resin, Podofilox (Condylox), Trichloroacetic and bichloroacetic acids, Imiquimod 5% cream and interferons) are available, which can be applied directly to the surface of the warts but they should be used after a dermatologist’s guidance. Other treatment options include electrical cautery, surgical removal, Carbon dioxide laser treatment and electrodesiccation.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.