oohhhhh I have done that - twice in fact and always the same finger no matter how careful you are, accidents happen particularly with little squirmers.
I just pop DD bleeding finger in my mouth once she has calmed down then apply firm pressure for as long as she lets me. I don't use bandaids despite the amount of bloodloss as it really doesn't take too long for her clotting mechanism to kick in.
Hoping your little man is ok today