The key proteins associated with fish allergy are Parvalbumins, found in most species of fish. It is found in different concentrations in different species of fish
Parvalbumin is a very stable protein, so able to cause reactions when cooked or as vapour during cooking (but food is thought to be 20-60% lower in parvalbumins when cooked). It is found in high concentrations in the light muscle of fish rather than the dark muscle, so fish like cod and carp are higher in parvalbumin levels compared to swordfish and tuna which have lower levels as they have more dark muscle tissue.
Parvalbumin is the protein used for testing, if you are negative to these tests then your allergy may be to less common proteins found in fish, namely endolases, aldolases, collagen and most importantly gelatin.
There is no information on syndromes associated with fish allergy.
Occasionally there can be cross reactivity between fish and products containing gelatin.