His and Her Circumstances

Yukino Miyazawa is really, really vain, and loves to hear people praise her. She's always been the best at everything, and always tries to look perfect. But when Yukino goes to high school, she's finally upstaged--by Souichiro Arima, who scores better on the entrance exams and instantly snatches the attention of the class. By accident, Arima finds out that Yukino is just pretending, and this starts off a series of events that lead to Yukino and Arima falling in love. They then have to cope with a lot of obstacles in their relationship.

Synopsis from Anime News Network