My daughter had a wart on her toe, and the doctor had me put duct tape on it for like two weeks. Apparently the wart needs air to avoid being removed by the immune system or something. It removed it, and she's never had another anywhere. You might search duct tape and warts and see what they say.
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. Other treatment options include electrical cautery, surgical removal, Carbon dioxide laser treatment and electrodesiccation.
In my opinion you should talk to a cosmetologist/dermatologist about this and get these warts evaluated. 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 dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.