 If you liked
Full Moon wo Sagashite
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 ...then you might like
Honzuki no Gekokujou: Shisho ni Naru Tame ni wa Shudan wo Erandeiraremasen Dai 1-bu - Hon ga Nai nara Tsukureba Ii!
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Ascendance of a Bookworm and Full Moon wo Sagashite are two manga series with a young and passionate female main character and some very cute artwork. The main character in both series really love something (books in Ascendance and music in Full Moon), but due to their age and very sickly nature (as well as due to the time setting in Ascendance's case), her family often limits her to staying at home and doesn't understand her interests. Ascendance isn't as tragic/dark as Full Moon, though.