Exposure to Jellyfish is a common problem observed among fishermen of northern Sri Lanka. Being a general physician I treat them with antihistamines and short course of steroids. I dont know the exact pathogenesis.
The interesting question is whether these reactions are mast cell mediated or merely toxic ones. And whether they may cause an anaphylactic reaction, in that case, what mechanisms are involved. Personally I am not awere of any specific allergy test.
From a practical perspective, antihistamines and short term steroids should be fine.
More informations about pathogenesis are well examined in the following article: Immunological and toxinological responses to jellyfish stings.Tibballs J, Yanagihara AA, Turner HC, Winkel K. Inflamm Allergy Drug Targets. 2011 Oct;10(5):438-46. In Southern Italy First Aid Centers we have got the same problems in summertime. Furthermore jellyfish can induce anaphylaxis even when ingested...