I read this fic a while ago and I am pretty sure that it was on fanfiction.net. I don't remember much about it, although it is an MA fic for sure. Oh and it is quite long, definately longer than 30k words.

Kagome was chosen by the council (using some kind of magical thingy) to be Sesshomaru's mate. He hates the idea and she isn't thrilled either and they put each other through hell before they get together (the fic takes the scenic route when it comes to romance so that doesn't happen for long time).
I remember the scene towards the end, where the two mate and Sesshomaru howls, announcing the mating. Inuyasha hears it and gives up on Kagome, instead he goes after a half-demon inu.

If anyone remembers it or any fic like it, that would be great! Thanks.