Hah, what is it about things on our hands that have us picking at them!!?? When I was younger, in my teens (like a zillion decades ago) I had a couple warts develop too and I was so embarrassed to show my hands.
They were on my thumb near the nail and also on the thumb joint. It was so hard to leave them alone!! But then realized they looked even ickier when I was futzing around with them…and hurt! My mom took me to our doctor and he used liquid nitrogen to freeze them off. That worked!