I recently finished reading "And Then" by Soseki Natsume and absolutely loved it. While it's about a ~30 year old in the Meiji period so maybe not exactly what you're looking for it did lead me to an earlier novel by Soseki called "Sanshiro" (the first in a thematic trilogy, "And Then" being the second, and "The Gate" being the third).
Sanshiro is a teenager, so more inline with what you want though also in the Meiji period.
I do think this period is a fantastic time to investigate because it is the transition from the traditional Shogunate government to a more Western style and the books deal heavily with how that transition causes tension.
Also, side note, Murakami wrote a fascinating introduction to Soseki's Sanshiro that gives a lot of praise to his work and importance in Japanese literature (though I didn't read the whole thing because I don't like to know too much about a book before digging in).