Thanks for writing your query.
After reading your post,it seems that yor child is having upper respiratory tract
The cause can be viral or bacterial and can be confirmed by some investigations like :-
1. Throat swab culture.
2. Complete Blood Count(CBC).
Red spots can be related to the fever
and needs clinical examination.
You should get him examined clinically by his Paeditrician.
He can be given antihistaminic like levocetrizine for cough
Any medicine to be given after discussing with his Paeditrician.
Encourage him to drink lots of pure water and to eat fresh fruits and vegetables.
Furthur treatment can be planned according to the reports of the investigations.
I hope this is helpful to you.