What coral was in an open wound? That might help us better explain.
Most of the corals in our tanks, especially the ones you mentioned, don't pack enough fire power to do much harm to humans though there are a few exceptions. I've certainly had a few whelts from hammer corals and anemones, but over time I've become more or less immune to the heavy hitters and don't really react any more.
That said, some people tend to be more sensitive than others to coral stings, sort of like with bee stings, but it's strange that you reacted so much to it. Especially the pain and paralysis. That's uncommon. Leathers and zoos are capable of toxicity but aren't known stingers. So that could be a possibility.
If you are one of the sensitive ones, keep some antihistamine handy and treat it as you would a bee sting. The whole vinegar thing is a load of baloney. If nematocysts that have not fired already are stuck in your skin, a change in pH (ie. vinegar) will trigger them and just make you feel worse. The best thing to do is to rinse the area with the same water they were in. Once they've fired there really isn't a whole lot you can do to neutralize the sting (though there are old wives tales abound about this... If you doubt me, go pee on your hand and see if you feel better... I can wait
).
Hope you feel better! A couple of years ago I was free diving and came up to the surface, right into 12 ft long, 3 ft wide jellyfish and got nice and tangled in the tentacles. I still have the scars from the resulting aftermath, so I totally know how it feels.