Hmmm there are a few that I can think of, but they don't exactly fit your description 100%...
SPECIAL A
Hikari Hanazono, the main character, has always been second to Kei Takishima. While Hikari considers Kei a rival and somewhat of a friend, Kei loves Hikari. Everyone knows this, but she is too dense to notice. Their wrestling loving fathers first introduced them to one another when they were 6 years old. Assuming that she was the best in wrestling, young Hikari challenged Kei to a wrestling match only to be thoroughly defeated by him. Ever since that fateful incident, Hikari swore to beat Kei in school grades, a sporting event - anything. To do this she has enrolled in the same school as Kei since elementary. Now she attends Hakusenkan, an ultra elite school, that costs her carpenter father a lot of money. Hikari and Kei are the top two students in the school, with Kei holding firmly to that number one position.
http://www.animenewsnetwork.com.au/encyclopedia/anime.php?id=8769
KARE KANO
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.
http://www.animenewsnetwork.com.au/encyclopedia/anime.php?id=392
It can be 'Special A' but Hikari's not hiding that she's poor and Kei is not a shy type guy. It can also be 'His and Her circumstances' but i don't think the guy is really shy. hmm.. i can't think of anything else. Sorry, that's all I've got.