Welcome to platform of Health care magic.
There is a history of whole family suffering probably with some viral infection.
In my opinion your child has also contacted some viral infection. Cold
all symptoms are pointing toward the viral infection.
He should be alright with couple of days provided his nutrition and hydration is not compromised and he should also be symptomatically treated for fever
If he does not respond in day or two. then one should investigate the child for any other problem.
Hope your query is answered