Salmon, tuna and halibut are the most common kinds of finned fish to which people are allergic.  More than half of all people who are allergic to one type of fish also are allergic to other fish, so allergists often advise their fish-allergic patients to avoid all fish. If you are allergic to a specific type of fish but want to have other fish in your diet, talk to your doctor about the possibility of allergy testing for specific fish. Finned fish and shellfish do not come from related families of foods, so being allergic to one does not necessarily mean that you must avoid both.