I was in the exact same position as you. 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.