Thank you for your query.
I feel you need not worry about the low white cell count as long as there is no problem with your son. As you have not mentioned the platelet count
I will not worry as long as it is above 40,000.
You have rightly mentioned about the bilirubin
that it is because of the Gilbert's syndrome.
I hope I have answered your query to your satisfaction.
Wishing your son all the best.
Rajiv K Khandelwal