Since returning home, we have been trying to determine several things: What stung her? Is she allergic, or was it merely a severe sting in a sensitive area? What can she do to prevent a fatal recurrence? Is there a way to test if she is allergic? We have also been told that the next time she is stung could be worse because she is sensitized - is this true?
Your experience is consistent with the sting of a Portuguese man-of-war (Physalia physalis). There are other members of the coelenterate phylum which can produce a similar reaction, but Physalia is the most common offender. The animal has a "sail" which floats on the surface and moves the animal in the direction of the wind. There are one or more long tentacles extending 33 feet/10 meters or more, and they are responsible for most stings.
In rough weather, the tentacles may become separated from the sail and drift just below the surface, where they are practically invisible. The toxin is potent enough to have produced the entire problem your wife experienced without an allergic component. However, the toxin is a potent antigen and probably produced an immune response so that she now may be allergic to the venom as well as susceptible to the toxic effects. Another exposure may consequently be more severe. Fatalities, however, are rare and usually appear to result from drowning because the pain and the sting's toxic effects sometimes weaken swimming abilities.
Prevention of injury is best accomplished by avoiding contact with the animal. They are frequently found together in large numbers. When many "sails" are visible, swimming or snorkeling is not a good idea. Since the man-of-war remains near the water surface, diving might be possible - provided it's done with great care during entry and exit. Protective apparel such as full wetsuit or thick dive skin prevents contact of the toxin-containing nematocysts. Keep in mind that nematocysts can remain potent for hours and be transferred from dive apparel and gear to bare skin when handled. If the wind is blowing onshore (from the ocean toward land) the animals are more likely to be present than with an offshore wind. In the event of a repeat sting, the EpiPen (which contains epinephrine) might modify the allergic component of the reaction, but it would not relieve the toxic effects.