Welcome to Healthcare Magic forum.
The description of your childs symptoms resemble that of a petechial rash
causing micro hemorrhages from tiny blood vessels under skin which is most commonly seen in viral hemorrhagic infections, bacterial sepsis
or rarely an allergic rash
.Considering he has been diagnosed with bronchitis
and has low wbc count the cause is most probably infectious and needs appropriate antibiotic and supportive therapy including bronchodilator
and anti histaminics.
Young children have an immature and developing immune system so they can have drastic effects of even minor infections.Please do not worry since most infections resolve soon without complications with timely and appropriate treatment.
Meanwhile please ensure that he has plenty of fluids to maintain his hydration along with a nutritious diet, and follow up with the doctors as per advice.
Wishing him a speedy recovery.