Hi, Rosanne and welcome!
My name is ***** ***** I will be assisting you tonight.
I'm sorry your kitten is exhibiting these symptoms. It's possible that she has fleas, mites, or another type of external parasites that are biting her and bothering her.
There is a neurological condition called feline hyperesthesia, which will cause a cat to suddenly start biting at her back, sides, back legs and tail. Sometimes, she will take off running like something is chasing her. Here is more information:
Symptoms of distemper are typically, lethargy, vomiting, diarrhea, dehydration and loss of appetite. The symptoms you describe do not fit this profile.
For the moment, I would comb her with a stainless steel fine- toothed flea comb and see if anything is in her fur; if you do find fleas, dunk the comb in a tall plastic cup of warm water in which you placed 2 drops of original Blue Dawn dishwashing liquid; that will kill them.
If your kitten is over 2 months old, she can be treated with a monthly topical kitten flea treatment sold by your vet, like Advantage, Frontline, Revolution, or many others. Just make sure it's sold by your vet. Do NOT ever use flea treatments from supermarkets or pet stores like Hartz, Sergeant's, Zodiac and others, as they are ineffective and have had fatal results in kittens and cats.
I would recommend a check up by her vet, asap, for your kitten, so you can get a definite diagnosis and treatment to help her feel more comfortable.
My best wishes that all will be well with your little, furry girl!
I hope you found my answer helpful and if so, please tell me and/or rate with positive feedback, as that is the only way I receive credit for my assistance. However, rating will not prevent us from continuing to communicate and you can ask follow-up questions at no additional charge.