Thank you for your query.
of eyes is due to the reaction to that oil.
Clean his eyes with clean sterile water and a soft clean cloth.
As the child is having cough
, they usually swallow the mucus and because of stomach irritation
by mucus or because of posttussive vomitings they vomit the mucus.
Consult your doctor for the examination of his eyes and medication for it including cold
Hope I have answered your query.