Thank you for your query at DoctorSpring.com
I can understand your concerns. This is indeed a common scenario. Rapid defervescence (fall in temperature after a high grade fever) can fool the body into thinking that child is losing heat quickly. Hence the body starts constricting all skin blood vessels making the child feel cold and sweaty. This physiological phenomenon has been exactly described by you.
This can also happen rarely with overdose of anti-pyretic drugs. If a high dose of these drugs are accidentally ingested, a cold sweat phase develops with body temperature plummeting into hypothermia. What us the weight of your child? What dose of ibuprofen have you administered? What formulation did you use?
Dr. Saptharishi L G