Hi, you didn't say what counts on his test were high.
But I expect you are talking about the WBC. That can be high from infection or from leukemia.
Also, if his platelet count is not low, then it is unlikely that his easy bruising is from a blood cancer.
I hope you get your call from the doctor soon with good news.
Yes I agree with Ken. You did not say what the actual blood counts were. Not that we would advise, but a high WBC is how they found my Leukemia. IT could also be a bad infection too. Make sure your doctor follows up with any further testing needed to get a actual diagnosis.