Did the wart on my hand give me Genital warts?

I have a partly shed wart on my right thumb. (due to me freezing it a week ago) But silly me and my hormones, I continued to ****. Today I found a little start of a wart on the place where my thumb would go when I would ****. I froze it, but is that a permanent fix? Should I consult a doctor? Did Righty just give my Willie Genital warts?