Hi welcome to health care magic forum.
Thanks for calling .H.C.M.Forum.
You have got the smell of burning tyre from your air conditioner while it is working. First thing you have to do is get the air conditioner repaired, Because the fumes must be coming from the air conditioner due to burning of the wires in side it .
If it is left like that it may continue to emit the same.
As the fumes are of the plastic they will be thick in nature and diposited in the nose and bronchial tree, and cause irritation of the respiratory system.
You have got headache and dizzyness
, you would have inhaled more , it may be cleared in span of 1 hour, if you dont get relief , consult a physician.
Regarding children if they are free of any symptom you don't worry , usually late symptoms won't be there.
Wishing that everything is fine.