Demon in the wrong time

Kayo Higurashi is Kagome's adopted sister, when Kayo was a toddler her biological family dumped her into the Higurashi's well, Kagome's mother found her and took the strange child in. She was found wrapped in a black and white robe that looked to belong to the feudal era. With crimson eyes,and long black hair, she didn't fit in very well. Then one day she and Kagome fall through the well, what happens when Kayo can't pass back through again and even finds out she's a pure bred dog demon? And what'll happen when she gets separated from her group and ends up meeting her real father? And who else to come but her new friends along with...Sesshomaru and he's gang?