The first one is "A Christmas to Remember" by Inufan1 (Rated T)
www.fanfiction.net/s/7614115/1/A-Christmas-to-Remember
"Tell me Higurashi, did you and the mythological Lord have tea together?" Her teacher asked sarcastically. "No professor, The Lord of the Western lands and I never had tea together, although we did spend Christmas together." was her simple reply. S/K
The second one is "Fateful Meetings" by Acissej123456 (Rated MA! NO YIM!)
www.fanfiction.net/s/7763670/1/Fateful-Meetings
Set in Feudal Japan. Kagome is an orphaned miko living on the outskirts of the Western Lands. One day, she finds an injured Sesshomaru in the forest and heals him. Her adventure begins as fateful encounters slowly draw her into the society of demons.
The part you're referring to is in chapter 20.