According to HowStuffWorks, some common symptoms that people who have fish allergies exhibit are skin swelling, nausea and diarrhea. It is possible for some people with fish allergies to have respiratory issues, dizziness and even to lose consciousness.
The American College of Allergy, Asthma & Immunology says that eight foods, including fish and shellfish, cause about 90 percent of food allergic reactions. Other symptoms of fish allergies include hives and a mouth that itches. Coughing, problems swallowing, blue or pale skin and wheezing can also be symptoms of fish allergies. HowStuffWorks points out that food poisoning presents many of the same symptoms as a fish allergy.