I have no idea what it is with me and the vampire stories lately even though I'm not sure that this one is. Sesshoumaru runs into Kagome one day and takes her blood then thinks nothing of it. He then discovers that no one other then Kagome can quench his thirst. Kagome finds herself drawn to him for reasons that she can't explain and they always seem to find themselves running into each other. I believe that there was a part where they went to talk to someone about it and he told Sesshoumaru that the only person that he could take blood from and survive anymore was Kagome. That's about all that I remember.

It sounds a bit like The Red Hunger by Bella J Cara. What do you think?

It's not that one, although I will be reading that one soon. It takes place in futuristic Japan. If that helps