MoonlightSerenade, I think I know the one you are talking about. Doesn't doggie Sess attack her in her kitchen after destroying her kitchen and tearing cabinet doors off, then he bit her wrist. She wanted a dog to help protect her, since she lives in an apartment in a bad neighborhood. Sess is in a emotional spiral and feels he lost everything but his name.
Canis familiaris by Tallymark
At one point, Kag’s has dirty dreams about Sessie and he can tell. Later, she goes out on a date someone else and Sess is pissed. She comes home to him in his human form and leaves cause she smells of another demon and didn’t wait for him. I think Sessie leaves after that.
She writes another story I like (and Honey-Bee helped me re-find) called Gone to the Dogs, where Kagome is the dog.