Hi Steph
If your cat does go outside it is possible she has been bitten by another cat at her tailbase. This would cause a swelling due to infection or possible abscess. It would make it difficult for her to get comfortable when sitting and she will be reluctant to hold the tail upright. You may be able to see the skin looking inflamed if you part the hair or possibly some scabs/puncture marks. If this is a cat bite she will do better with some treatment from the vet.
If the tail is completely limp and has no tone and she has no control over it, it is possibl broken but this seems less likely. She could have trapped it or crushed while out and about. Again this would be best to seek veterinary attention for because it may not repair on its own.
Hope this helps, and hope your little cat makes a quick recovery
Cat Veterinarian
MRCVS, BVSc