My kitty got the very very tip of his tail in the front door I closed it.

There was a fire very close to our house. I saw the planes outside the window flying so low and ran outside to see plumes of smoke about 1/2 mile away! Coming back into the house, he somehow got it in the door when I closed it.
He didn't meow or anything, but ran into the bedroom under the bed. It oozed a little blood and looks like it might have pulled all the full off the end and maybe the very very tip of his little tail.
He didn't act like anything was wrong. Let me handle him. Wasn't crying. I wiped it off a bit with a damp paper towel. He's been eating and drinking.
This morning it's clotted on the end with the fur. He's licked it a little bit and seems to be sleeping with his paw or head over the end of his tail.
How worried should I be about infection? Does this require a vet visit? (Unemployment has taken it's toll and if I can handle this without a vet vist, that would be preferable.) Does it need to be bandaged? I imagine some bandage that doesn't stick to fur? But then how would it stay on the end of tail?
My poor poor kitty. I feel terrible.
Now for the weird part. I had a dream the night before this that my cat lost his tail due to some incident with a dog. I didn't know I was the dog.
(and in case you're interested, the fire was out very quickly. The wind was blowing away from us. They had mulitple planes, a helicopter and from what I read, ground crews:
http://tcfireweb.co.riverside.ca.us/...tHtml&id=27323 )