Red sore patch on cats tail :/

My cat has a red looking bald patch on her tail. There are no signs of fleas on her coat. Any idea what this could be?

She winces if I try to examine it and runs off. She seems in good health and spirit otherwise.

We got a new kitten last week... Though I am pretty sure this started slightly before.. But can't be sure. Could this be connected?

I'm booking her in to the vets for Thursday.

Does the kitten have any bald spots? One possibility is a fungal infection like ringworm. Another is overgrooming on her part because the change in the household is causing her a bit of anxiety. Getting her checked by the vet is a very good idea.