Oh yes please take kitty to the vet immediatly!!! When I was little the same thing happened to my kitty (he got his tail in the door hinge and we closed the door not knowing) and the vet had to shorten his tail a little. We did not have lots of money, so the first day my dad just wrapped it up in gauze but kitty kept chewing it off. So the vet removed the end of the tail and stitched it up nicely the next day. Please keep us posted!