Kerosene is a volatile hydrocarbon liquid.
Because of this nature, the inhalation of kerosene vapors can lead to various complications involving the respiratory system & central nervous system
...such as coughing, sore throat
, headache, confusion, unconsciousness
So...the symptoms as mentioned in your post can be attributed to inhalation of vapors of the spilled kerosene.
Management involves movement to a safer place to avoid continuous inhalation of the harmful vapours, breathing of fresh air & symptomatic treatment.
But if symptoms still persist or aggravate, then it will be better to consult your Doctor to rule out other causes of vomiting
Wishing you a speedy recovery.
Thanks & take care.