Since you have not found anything sticking out of your toe, you can assume that either nothing actually entered the skin, or a piece of wood did become fully embedded under the skin. In either case, this does not present a problem for mikvah and is not considered a chatzitzah.

During your chafifah we do recommend soaking your toe in warm water and seeing if anything comes out. If a piece of splinter does emerge you should do your best to remove it, or at least cut off any piece that is protruding from your skin.

Please feel free to get back to us with any further questions.