Greetings. Welcome to the healthcaremagic. Baby oil usually contains synthetic hair oil with mild ingredients then adult hair oil. When ingested it can cause different problems depending on the exact composition, amount and wether it was swallowed or it went into the airway. In your case the cough developed latter which suggestes that oil probably caused irritation of the throat and nothing else which is causing the cough. In that case its nothing serious . Just observe and take care of increased throat irritation. If the oil has gone into the airway, which is less likely because then coughing would have started at the very begining and would have been severe. Final consequence would have been pneumonia, bronchitis etc. Therefore if the X ray is fine then there is nothing to worry about.Just an anti histamin syrup will be enough. I hope the answer was helpful. In case you need any further assistance feel free to contact in writing. Regards Dr Talal Hussain