It seems unlikely that you would be allergic to sea water as the salt isn't an allergen and the fish or algae wouldn't impart enough allergen into the water to cause a reaction. Aquagenic Urticaria (allergy to all water) is extremely rare (less than 100 cases have ever been reported). You may have Cold-induced urticaria when the wet skin cools rapidly and causes urticaria outbreaks or Cholinergic urticaria, perhaps from exercising (for example swimming) and then sweating afterwards when out of the water.
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