Peeing on a jellyfish sting aggravates the nematocysts and causes more of them to fire, intensifying the pain. Rinsing the area with sea water will deactivate the stingers and bring some relief.
I've never heard of anyone being allergic to jellyfish... That's definitely a new one, but I hope you feel better OP and are able to salvage what's left of your vacation.
A jellyfish is a venomous creature that uses stingers to incapacitate prey with a neurotoxin. It's the chemical make up of the neurotoxin that some people are allergic to. Most people breakout in a painful rash for a couple days.