Manga about WWII in Japan
The year is a little bit off but I think it's Hadashi no Gen



It's a manga series by Keiji Nakazawa. The series takes place in Hiroshima during the final months of World War II. The main character is a boy named Gen Nakaoka and his family live in poverty. It shows an atomic bomb attack in Hiroshima on first volume, where Gen's father and siblings perished in the fires, but Gen and his mother managed to escape. 


  There's a scene where one boy (I believe he's the main character here) is fighting with his friends, and I think his friends are bullying him, and that boy bites the friend's finger off and eats it later


It's probably this, he ate the finger afterward.



As you can see, the art is not like most shounen manga around 2000. It's because this manga was serialized from 1973 to 1985. It was published at late '90s in my country so I guess there is a possibility that this is the manga you mentioned.