I remember reading a story in 5th or 6th grade about two brothers where one was jealous of the other. The elder brother had polio in one of his legs and when they were playing gulli-danda, the younger brother was not chosen in any team whereas the elder brother played very well. When in anger the younger one beat the gulli against a rock, it deflected and hit his own head. He ran home, still bleeding and lied to his parents that his brother had hit him. This is a Hindi story and was published in a literature book for class.
It's a short story by Uday Prakash called "Aparadh" and it appears in a Class 5 Hindi textbook called Garima. You'll find it here.
I found it by doing a Google search in Hindi for gulli danda "पोलियो" kahani, with polio in quotes (which makes it search exclusively for results where the quoted word or string of words is found verbatim) and also in Devanagari. I think I found the Google Books result on the second page. The first paragraph of the story it took me to contained a lot of the details listed in the OP: the narrator says he had an older brother who had polio in one leg but was regardless great at sports. A quick scroll to the second page shows a picture of a boy getting hit in the head during a game of gulli-danda. The next page's second paragraph is just a single sentence where the narrator says he told his mother that his brother had hit him with the gulli. There's a picture beside the text on this third page showing a boy with a bandage around his forehead being comforted by (presumably) his mother, with (presumably) his father glaring at a tearful older boy in the background.
These details, as well as the fact that the book the story appeared in was a Class 5 textbook, helped me confirm that this story was the one you were looking for.