Rash of measles
is usually preeceded by fever
and rashes starts from face. You have not mentioned the immunisation status of your child. Even after immunisation measles can occur but that is mild in nature.
This rash can also be due to soap allergy
So I would suggest you to stop using this soap and give him syp. zinc which will help in recovery from cold and cough
,also apply calamine
lotion if there is itching. Even if it is due to measles only conservative management is needed like maintenance of hydration and temperature.
Also consult your doctor for clinical examination for rash and to evaluate for long duration cough.