Hi

In the story, Kagome is Sesshomaru's fiance but he seems cold towards her.
She broke up with him at the restaurant on their date.
As it turns out Sesshomaru is quite insecure and didn't talk to her much because he is afraid to say something wrong to her.
He thinks that she left him because he showed up at her place too early for their date.

Thank you so much for all your help.

I think you are looking for Misunderstood Silence by Himura Asami.
He stayed quiet out of nervousness, not disdain, but she wasn't a mind reader. After seven years, it was only natural for her to get fed up. she broke off their engagement, and now he's going to do whatever it takes to get her back.
Rating: K+ - Universe: Alternate - Status: Complete - Category: Oneshots - Genre: Angst, Romance - Updated: 07-11-13 - Created: 07-11-13 Chapters: 1 - Reviews: 7 - Words: 7,026 - Reads: 2,577 - Anonymous Reading: Yes

Yes! That's the one. Thank you

You're welcome