Thank you for your query on Healthcare Magic.
If there is no signs of bacterial infection and fever usually antibiotic (advent) is not required.
For cold you can give oral antihistamine drops like chlorpheniramine
with the Pediatrician
For cough mucolytic
oral drug like ambroxol
If there is any nose block, you can put saline nasal drops into nostril whenever required.
Use domstal in prescribed dose for vomitings.
Hope I have answered your query.