I found your story interesting and, in my opinion, your Sesshoumaru is fairly good. You keep him impersonal and introverted. I won third place for 'Best Sesshoumaru Portayal' and have been told I 'channel' him so if you need some inspiration, just look over my 'A Debt to be Paid' or whichever story at the Sesshoumaru parts. The key to Sesshoumaru is to make him not give a flying rat's bum. He does not care, will not care and if he ever miraculously does, he will deny it and hide it. He is capable of few things feelings wise; loyalty, disgust, hate, impatience and intrigue. Rin is the exception. Remember, he didn't cry when Rin died later on in the manga, so incapable of expressing emotions he is, that Jaken cried for him.
Sesshoumaru is a difficult character to portray and especially is hard to pair with Kagome if you chose to keep him as in-character as possible just because they are so opposite to one another; an introvert and an extrovert.
My own observation for your Sesshoumaru is to keep him distant, keep him cold and make him fight against any acceptance/feelings/realizations he has for Kagome. He has too much pride and is much to ignorant to emotions for him to ever easily accept that situation if it ever came to be! Good luck and I like your story so far
