Is white blood cell count 13500 high for a 6 year old ?

No: That total count is within normal range, but total number is not the only thing to consider when looking at a WBC count. You need to look at different types of cells present and the clinical picture. It would be on the high normal side if the child is fighting a viral infection, but totally normal for something like an ear infection. So put all pieces of puzzle together before final determination.