New wart, under the skin, how to stop it early?

I've had warts passed through my family, from my son to my wife to me, and am finally getting rid of the one on my left thumb by a mix of 40% salacilic acid pads for a day then filing with a new nailfile until it bleeds and hurts, then putting on a new pad.  Its very close to gone.  However, to more have appeared on my right hand, index and middle finger but they're under the skin so I can't do much.
Should I try freezing?  A wartabater?  I work with my hands and have to frequently wash them, so wearing wart pads is difficult so I need this gone ASAP.  I had them frozen at the dermatologist, also cut (more like shaved) but again, these new ones are still under the skin and I don't want to wait another 3 months for them to surface.  How do I deal with warts still totally under the skin?

[Dr Santos]

Hi,

Warts are caused by a viral infection specifically by the  human papilloma viruses (HPV). They are contagious and spread when the virus touches a part of the skin where the outer protective layer is broken, either by minor trauma or by moisture. This happens most commonly on the fingers, elbows, knees, and the bottoms of the feet. It is also possible to get warts from using towels or other objects. They typically disappear after a few months but can last for years and can recur. Topical treatments containing salicylic acid were the best treatment according to a study done. Gentle freezing, on the other hand, to be effective, must be done at least  4 times. Several newer treatments aim to boost the body’s own immune response, including Imiquimod cream or alpha interferon injections. Being a virus, the wart can easily be eliminated with active immune systems. (http://en.wikipedia.org/wiki/Wart)

Take care and keep us posted.