i wish there was a longer story that has to do with a physically disabled character. it do...

Try koe no katachi

You probably read this one but oh well
http://www.mangago.zone/read-manga/hidamari_ga_kikoeru/

Also:
bad leg, dark story: “The Dragging Sound” by Harada
paralyzed, dark story: Agnus Dei
Deaf character, very good: Jouzetsuna Yubi http://www.mangago.zone/read-manga/jouzetsuna_yubi/

Blind character, very good: http://www.mangago.zone/read-manga/harem_days/mf/v01/c004/

Guy seems developmentally disabled, excellent and complex: http://www.mangago.zone/read-manga/i_cant_even_breeth_without_you/

Brain damage, sad: http://www.mangago.zone/read-manga/restart_harada/

blind, fantasy: http://www.mangago.zone/read-manga/dokunoaji/

albino and developmentally disabled, this is dark/tragic: http://www.mangago.zone/read-manga/bannin/

There are some more that I can't think of, a recent one with a kid with brain damage (but that one is so depressing). There's a historical yaoi with a guy with no arm (forget the name). And one where a guy has his arms cut off (weird). I don't remember these titles.

If mysophobia counts as disabled for you: Ten Count

Thanks for turning me on to such an incredible manga! This is a great story and one that touches me deeply since I am also hearing impaired.