Hey there. Which part of the tail moves - the top or the bottom? It doesn't sound like a tick as you would see a tick and they present differently. Having said that having you noticed anything abnormal about the cat with walking, breathing, panting, lethargy, vomiting etc. If yes, I would consider taking her to an after hours vet.

It actually sounds to me like your cat has broken her tail or the like. Is it the end part that hangs limp and doesn't move. If you touch just the end is it painful? If she doesn't react try higher and higher up until you do get a reaction. If you don't get a reaction at the end try giving it a tiny pinch with your finger and thumb. If you get no reaction she may have lost feeling there. If she is feeling pain at least you know she still have nerve function.
How is she feeling otherwise?