The Brothers Karamazov question

I need to find this book about a boy who has a younger brother who is mentally disabled (autism, down sundrome, ect). He is sometimes embarrassed by his younger brother. One day, he was with his little brother and his friends, and his little brother fell into some ice. Instead of the older brother helping him out, the younger brother who was mentally disabled had to get out himself and walk home. He later got pneumonia and died from it right before Christmas. Christmas came along and the older brother opened a present from his younger brother. It was a letter saying how much the little brother loved him and how he wanted to be like him someday. Somewhere in the book, the older brother said, "I am not my brother's keeper". Read 20+ years ago. Email me at desiforemperor@gmail.com.