My dog is frequently twisting herself around

It's almost like she's trying to gnaw or scratch at her butt. Her name is lily and she is an 8.5 year old Jackrussel-pug. She has also been biting and licking her paws along with the other 4 dogs in the house. I have the whole thing on video but it won't let me send it, this is the best picture I have.

Hello.  Biting and licking at paws can be a sign of skin disease, and so can biting and licking at the delicate skin of the anus, where the anal glands discharge.   It is most commonly conected with allergic skin disease.  There are other possible reasons - for example neurological ones - but your vet will talk over the most likely possibilities with you and take it from there.