IS my cats tail broken??/?

I accidently shut the door on her tail, But when she walks her tail is raised up high!

How do I know whether her tail is broken or not?
No I dont think it is broken. just hold on to an eye on it and monitor its symptoms. Your cat should be fine.
My cat won't sleep within her bed...
Since her tail is raised, it's not broken. A broken tail would drag. Watch for swelling, bloody urine, or behavioral issues like hiding. If you notice any of these, she desires to see a vet for further evaluation. Be careful!
I am living my kitten beside another...
Answers:    Feel along the whole length of her tail for any bumps or kinks, if you find nil and she does not flinch with pain then the tail is probably ok.

She could be holding her tail up elevated either because the tail is a bit sore and bruised and she finds it more comfortable to have it like this for very soon or because she is so happy to be on good terms beside you again.
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