Got a cut on "wart" on my finger.. HELP?!?

A few years ago i got a splinter on my thumb & i thought i got the whole thing out. Since then, it looks kinda like a planters wart or something on my thumb & it wouldn't go away. Well about an hour ago, i accidently got a niiiice cut right where it is & it bled REALLYYY bad & wouldn't stop bleeding. (it's still bleeding a little).. So i let cold water run on my thumb to get the blood off & i could clearly see white stuff (kinda looked like dead skin or something) in the inside of the cut/wart. I pulled it out with tweezers & nail clippers & now there's a small hole in my thumb & it hurts really bad.. What should i do? Does it sound like it was a wart or something else? Is it gone now that i got that white stuff out?? Please help!! Thank you!