the protagonist is a guy who has some physical problem ? when he was a child he fell from a tree, and since then his best friend ignored him, then we find out that this childhood friend was feeling guilty because it was his fault that the protagonist fell from the tree and in the end they end up together, please help me I'm desperate

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"Un vero uomo si dovrebbe alzare per lavare i piatti"(cit. caparezza)

Bokura ni Matsuwaru Etcetera
Kakko Warukute Kakkoii Kimi - Not exactly an 'accident' but kinda fits your terms?
Toki no Maigo o Sagashite! - Not an exact match but pretty close.

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"For in all the world there are no people so piteous and forlorn as those who are forced to eat the bitter bread of dependency in their old age, and find how steep are the stairs of another man's house. Wherever they go they know themselves unwelcome. Wherever they are, they feel themselves a burden. There is no humiliation of the spirit they are not forced to endure. Their hearts are scarred all over with the stabs from cruel and callous speeches."

they're not the manga I'm looking for but they seems interesting , I'm going to read them thank you

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"Un vero uomo si dovrebbe alzare per lavare i piatti"(cit. caparezza)

hmm, sound similar to Shadow oneshot in Renai Junkie

yes it's Renai junkie! thank you!

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"Un vero uomo si dovrebbe alzare per lavare i piatti"(cit. caparezza)