I had a few warts that looked like skin tags
too. I thought thats what they were for
a couple of years, but I finally got the courage to go see the doctor and lo and behold, they were warts. So, it's very possible that your doc is right. Good for you to see your doc quickly. I wish I had.
Right now, it is very possible to pass on the HPV virus. But, if you go about 6-8 months without reoccurence, it's a good bet that your immune system has suppressed the virus into a DORMANT stage.