She has about 10 on her hands...some really big and some much smaller around her nails. Our pediatrician suggested just letting them go away on their own, saying that they could only freeze them with the same solution we'd already tried OTC and that most warts only lasted for around 7 years....WHAT?????We have tried freezing, the wart bandaids, duct tape and finally the vinegar treatment. The vinegar actually worked, but you have to put some vaseline or neosporin around the wart before putting cotton soaked in vinegar on it, that vinegar will eat at the regular/non wart skin too and hurt.
We did this for maybe 2-3 weeks and they all turned black and she picked them off.....sadly every one of them came back within 4 monthsShe has about 10 on her hands...some really big and some much smaller around her nails. Our pediatrician suggested just letting them go away on their own, saying that they could only freeze them with the same solution we'd already tried OTC and that most warts only lasted for around 7 years....WHAT?????
Who wants a wart for 7 years!!! I once had a step brother that had a TON of them too, and his went away on their own....I think he'd had them for about 5 years though....so again, long wait.
Both my DD had warts on their hands. We soaked a tiny piece of a cotton ball soaked with apple cider vinegar and covered it with a band aid and then kept it on overnight. We did this for a couple of nights. In about a week the warts fell off. Pain-free and highly recommended method.

I swear, it was gone with a week. Try it... and let me know. 
We tried over the counter, freezing and smothering with duct tape all in combination. No luck. So we went to a podiatrist and he prescribed carac cream. It is supposed to be used as a chemo cream for skin cancers I believe but it really worked. Hers was so deep they said if it didn't work they would have to cut it out. We treated at home and it was gone in 3 weeks.
We apply some cream every night. So far it is getting better. We see the Dr every 3 wks so he can scrap the skin off. The dr did stress that if our copay was extremely high when we filled the prescription to let him know and he would help us get the cream. Yes, I have heard of cancer treatments on warts. Good point.We used a similar cream thst was a treatment for skin cancer for my daughter's Molluscm (sp?) they are like tiny warts and a caused by a virus as well. The dermo said that they are often misdiagnosed as warts and do not respond to conventional wart treatments (freezing, burning ect) she had 30 or so on her tunk area mostly and after a month or so of 3 times weekly application we got all of them. we were told to put the cream on 5 or so at a time untill they became red and inflamed then move on to 5 more. ther cream is supposed to stimulate the body's immune response to the viurs.
Warts do eventually go away by themselves. Sometimes it takes awhile for the body to recognize the wart and take action. My doctor informed me it could take up to ten years!
Yes, indeed. DS's one wart is 3 inches long on one finger and he plays piano. Egads!Unfortunately, this is not always true. I had the same tiny flat wart on my hand since I was in my early teens (I am 35 now). It went away as a side effect of my treatment. My Dad has had a small one on one of his fingers ever since I can remember. It is better to treat some kinds of warts as they may get worse and spread and the type of warts I had around my nails can permanently damage the nail bed over time.
I didn't see it mentioned here so I'll share my method.
First, good luck. I had terrible plantar warts when I was a kid on the bottom of both feet. It hurt to walk. Went to a podiatrist and he did the freezing and scraping thing. He also made a weird suggestion. I also had small warts on my knee and he suggested using a potato on them. Every night before bed, I cut a hunk of potato and wiped the flesh part on my knee warts. Within 2 weeks they were all gone. I had those warts for almost 2 years! No, I didn't bury the potato in the garden like the wives tale. LOL! I just wiped the white of the potato on it, put in in a zip baggie and used it again the next day.
The Dr, said there is an acid in the potato that kills the wart. I also used it on the plantar warts and they stopped growing. A few small ones went away.
Good luck!