More likely that you got stung by a bristle worm or two and now the water is irritating the stings and causing an infection. You could have stuck your hands in this tank a million times without any issues, it still doesn't mean that you're safe from infection if you have a cut, especially a very irritated cut or sting caused by something like a bristle worm.
If you have health insurance, I'd go to the ER just to be safe, especially if it hurts as bad as you say it does.
Some people are more sensitive than others. Keep in mind that there is a lot of bacteria in the water in our fish tanks. This is why it is suggested, although no one, including me listens, that we should where gloves while handling things in the aquarium.
Corals can cause wounds for the record. While I was in Turks and Caicos, I accidentally brushed my back against a large maze brain. The sting/cut didn't hurt bad at first, but it ended up getting very badly infected and I have a permanent scar from it along my spine. My mother also brushed against one and she was fine, so it all depends on the person.
