for example she was involved in car accident before or she has disease or been bullied? please recommend some dramas for me and thanks in advance ;)

What about Stand Up? (Maybe this counts as a spoiler and if it does, sorry, hope you don't mind.)
35 sai no Koukousei
Cat Street (more of a traumatic past)
Guilty Akuma to Keiyakushita Onna

Himizu is really weird and it only when you see the main female leads mother is when you understand why I picked this movie.

Innocent Love
Love that makes you cry (on your current watching list)
Innocent love, Kingyo club, MARS (I watched the taiwanese version and it was good. So I think the japanese version will be good as well), Guilty Akuma to Keiyakushita Onna and Byakuyako.