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My answer is yes, you should give it a day or two of observation as it is possible that your child might be on a recovery phase of a viral infection which started as an URTI then gradually caused acute bronchitis
and associated stomach irritation
. If diarrhea
, give him much water to drink say 500 to 1000ml daily together with ORS. If the cough
still persist, then its time to see the pediatrician
within the next two days before it gets further complicated. He should normally be completely recovered within the few days that follow if not, then we are probably dealing with bacteria infection that will require a course of antibiotics.
Hope this helps