Thanks for your query.
The boy is most likely having viral respiratory infection
These spots could be because of allergy
to any ingradient in benadryl
Also possible these could be due to the same virus that is causing cough.
If he is not having high fever
or breathing difficuly & otherwise is generally active & eating reasonalbly ok you can wait for a day or so. Avoid further doses of benadryl & if the rashes are really itchy can try atarax syp in appropriate doses.
Hope you find the information useful