Mike, this sounds very classic for an allergic reaction. The swelling/itching of the eyes, the hives that itch, the sudden onset all over the body, are all very classic for an allergic reaction. The next question you may have is--what am I allergic to? That, of course, is the million dollar question. Since it's only happening twice a year, it may be difficult to nail the offending agent down (but there are many things one can be allergic to, such as weeds, grasses, molds, trees, animals, perfumes, foods, lotions--the list goes on and on).
However, because it only happens twice a year, it may also be easier to catalog what you've done those days, what you were exposed to, what activities you were doing on those days, who you might have been around, etcetera to nail down the offending allergy-causing agent (allergen).
Above all, however, if you (yourself) are not able to determine what this agent is, you can always go to see an allergy doctor to undergo systematic allergy testing that may help you discover what it is that you are allergic to.
If this is significantly distressing to you, you may consider starting an oral antithistamine pill that you just take once daily, every day, as a preventive measure--good examples of these include loratadine or ceterizine (brand names are Claritin and Zyrtec in the U.S.).
Does this make sense? Does this information help address your concerns?
Do you have any other concerns or questions about this topic?
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My opinion is solely informative and does not constitute a formal medical opinion or recommendation. For a formal medical opinion and/or recommendation you must see an eye doctor. Thanks for your inquiry!