Hi. I understand your worries. He is on the right medications. So relax . Continue the medications and wait for 3 days .
Next Steps
Give him warm liquids / soup to drink frequently and do steam inhalation if possible. Nebulization is given for wheezing, if your doctor thinks he as wheeze then nebulize, , no harm.
If only cough ,then do not nebulise.
Health Tips
If cough not settling in 5 days and mother is also sick, then better get a COVID-19 test.