Stray kitten with unusual tail injury

We own an adult cat and a kitten about 4-5 months old, both female. They are both quite healthy tabbies. Yesterday we found another kitten in our open garage, a stray. It is a female grey and white long hair with an angular face and very skinny. It seems a little younger then our tabby kitten, Talia. It was so dirty we gave it a bath. It is very shy but is fine with being picked and held, even on her back. However, there are three things which are bothering us.

First of all, about three inches of her tail tip is nearly hairless. It is continously wet and slightly bloody. However, she shows no sign of pain and can move up and around with ease, though she has an unusual tail carriage, even when she is relaxed:between her legs near her anal area. Also, her nose is slightly runny and her anal area is red and slightly swollen. Her eyes are fine. She has been eating and drinking dry catfood and water. She is very lethargic and just wants to sleep, though this could be simply because she has been on her own. The third thing is that she refuses to play or pounce. Never once has she batted or crouched before anything, while our other kitten, Talia, rolls about in the straw, biting and batting and stalking it. I tossed the stray kitten a small handful of straw, which landed on her back. She didn't even try to shake it off. Someone nearby said that they had seen her eating a mouse a week ago. Is it possible she is no longer interested in chasing because she has done the real thing? We think perhaps was away from her mother to early or something similar.
Thank you for your time.
P.S. She refuses our warm cat basket. Instead, she climbs under the fence into the chicken coop, in which she spends most of her time licking herself or sleeping. she has not once chased anything, even chickens. It seems un-natural for her age.

Answer by Kate
Hi
yes there is definitely something wrong here. She may have some nerve damage, she sounds like she may have an infection and possibly even a cold or cat flu. As for her tail that sounds to me like a parasite problem which has caused her to bite her fur off and cause it to bleed.

Stray kittens can be prone to all sorts of illness es and really she need to be taken to a vet to be treated properly for all these things. She has had a poor start in life and now needs some extra care and attention to help her get back on her feet and give her the best chance of a life.

I'm sorry but i really do think your best option is to take her to the vets as soon as possible.

i hope she is better soon
best wishes Kate

---