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!

So my suggestion for you is to try and leave the warts alone to keep from irritating them. However, there are some safe home remedies for removal with potentially good results.
Besides the other 3 sites I found for you, here’s another with some more beneficial information.
https://www.health.harvard.edu/diseases-and-conditions/how-to-get-rid-of-warts
Have you tried any wart removers?