How can I stop my kitten from chewing on the end of her tail?

I adopted two 4-month old kittens, who are brother and sister. Ever since I brought them home, the girl has been chewing on the end of her tail. This is not all the time, but happens often. She's been checked for fleas and mites, no sores or open skin … the fur at the end of her tail is just very short from her doing this. I'm thinking this is just the stress of getting used to a new home, and missing the people who taken care of her since she was found without her mom at 2 weeks old. Please, any advice would be appreciated. The vet wants me to put this plastic cone around her neck, but I just know she will be miserable. Any help please…