The premise of the story is interesting.  You came up with a fresh idea, having Shippo die saving Kagome from Kikyo and Sesshoumauru bringing him back to life with tenseiga.  The first chapter is engaging and readable with a few misspelled words and grammar mistakes that are easily fixed.  But the second and third chapters felt very rushed to me.  It didn't seemed like they had even left the village before Kagome was attacked by the demon. Sesshoumaru saving Kagome fit fine, but his new found feelings for didn't make sense.  The first time he helped her it was because she reminded him of Rin.  That would still make sense for his second rescue.  For him to feel deeper feelings of love toward her needs to develop over time not that suddenly.  Chapter three had much the same problem.  Why put her some place where it would be logical for her to use whatever kimono was around and then be angry because she picked his mother's?  Everything moved so quickly that his actions don't make sense to me.

I'd revise chapters two and three.  Slow down and develop your plot more.  I recommend getting a beta to help with grammar and spelling mistakes as well as someone to bounce ideas off of and help keep the plot on track.  Every writer benefits from beta help. This tale has awesome potential and just needs a bit of work. 

The plot line has potential but all three chapters seemed a little too rushed. Kagome could never melt Sess' heart in one day, only to have him yell and chase her out the next - it's just not believable. Where were Sango & Miroku & Kaede?? Why would InuYasha just let her walk away? There are a lot of story inconsistencies to fish out but I urge you to take the time and outline the chapters, get a beta to help with the spelling and sentence structure issues and add as many necessary details as you can - in this case, more is always better. Take your time and have fun...the story will flow and we will all love reading it.

The story started out pretty decent, and with a bit of work could turn into a really good story.  Your sentence structure for the most part is really good, though there are a few sentences here and there that could use a little rewording.   A bit rushed, but good use of details.  Do try to stay away from using words in all caps or ()'s in the middle of your story, as they tend to distract a reader rather than adding to your story.  And there were a few spelling/grammar issues, but all and all, it is a very good start.

You have a good base for your story here, however you really need to slow down and explain things a little bit better. Your details are lacking and it makes it hard to follow the flow of the story. Some of your facts also don't seem to line up: in Chapter 2 he was happy with her and whispers her name to her lovingly, then in the next xhapter he treats her rather coldly, then gets mad at her for wearing one of his mothers Kimonos, and then kicks her out of the castle...The facts are inconsistent, this is where a little detail would come in handy to help explain why his attitude would go hot and cold towards her so quickly. There were a few spelling and grammar errors, but that is nothing a quick edit won't fix. You have a good start here, if you take your time and plan everything out, and most importantly don't for get the value of details, you will turn this into a captivating story. I wish you luck, in this, and all of your future endevors.

Wow, Sessy's attitude sure is changeable, one minute cold, the next happy, the next psycho...I think he needs some meds...

Anyways, I think you could benefit from finding a good beta. You have some word usage errors (example: saunter - this is a very casual stroll or walk, not what she would be doing after being attacked or carrying Shippou's resurrected body back to the village) or brake instead of break. Other than that, you are doing an okay job. Try to slow down, explain things more, go deeper into character thoughts and try to plan out the scenes in your head in greater detail before putting them down on paper, it will help and will expand the scene and flesh out the characters a little better.

You have a great imagination. Keep it up!