Sorry for delay.
You asked"Whats the diagnoses? "
There are multiple possibilities which could have possibly caused this:-
As you mentioned that the boy does not have any symptoms besides sore throat,cough and bruising ,it looks most like that he got a viral
infection in which a lymphocytes are increased and sometimes viral infection leads to decrease in platelet count so that may lead to bruising.
Sometimes even children with viral infection may also present with idiopathic thrombocytopenia so that leads to bruising and similar symptoms like your son.
Now other possibility could have been a leukemia which may also present with increased lymphocytes ,sore throat and bruising but it also presents mostly with weight loss,night sweats,swelling of lymph glands and lymph nodes which you denied so i am assuming thats not the case here,but always better to rule it out by just asking your physician to look at peripheral blood smear of your child for any abnormal looking lymphocytes.
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