R.J.
Half my family is "allergic" to tylenol.
It's technically not an allergy / not a histamine response, but a reactivity to it on a neurological level.
Starts off as a bad reaction (hallucinations, heart palpatations... moves onto heart attack and stroke). Their bodies react to acetaminophen/paracetamol the way most people react to stimulants. It's not normal. It's a quirk of neurology. ((Also why there isn't any ONE med for depression/adhd/bipolarity/etc. People's neurochem is all slightly different! So different meds react differently))
People can be allergic or have bad reactions to ANY substance. Because everything (from peanuts to bleach to insects) is made up of chemicals, and our bodies react to chemicals differently.
Personally, I'd do an empirical test:
Give the ibuprofen when your baby is 100% WELL. Because what you describe sounds like normal bleary sickness. If it happens when they're WELL and given the med... then it's time to contraindicate it.