I Went To A&e With A Suspected Broken Finger, It

I went to a&e with a suspected broken finger, it turned out my mail was just bruised after I trapped it in a car door...it went black then green and now it's black with an outline of red and purple and the middle is white...the doctors said black green purple and red was to be expected but what is the white bit? Is this normal or should u go back to the doctors?