Neck and Neck (2002)

Blurb:
Dabin Choi is the daughter of a man who runs one of the most powerful crime organizations in Seoul. She’s a martial-arts maven who’s full of energy and determined to use it. Eugene, the son of her father’s friend, who helps out with Mr. Choi’s 'business,' is also Dabin’s long-time unrequited love interest. When Dabin asks her father for permission to transfer to Eugene’s high school, Mr. Choi, ever the doting father, can’t refuse. Now Dabin is in the perfect position to woo Eugene, a role she has been dying to play. This seemingly perfect love match has just one flaw: Eugene isn’t into Dabin. In fact, he thinks of her more like a little sister. (The kiss of death!) Aside from this little romantic hiccup, there’s yet another obstacle for Dabin to overcome: her new classmate is none other than the son of her father’s long-time rival, Bongchun Myoung, Shihu, who she used to be friends with until their fathers had a falling out ...

Source: www.anisearch.com/manga/5089