There is no silver bird oil. It is EUCALYPTUS OIL and silver bird is a brand of the eucalyptus oil. If you are asking if the silverbird brand is good. Yes but mostly when used as drops on clothes or for steam inhalation (dropped in boiling hot water). Not for internal consumption

There's a chance your baby is reacting to the silver bird. To clear your doubt, please stop using it.

The second step you should take it to see a doctor as soon as possible because there might be other underlying health issues. Please treat as urgent