Antibodies don't have to bind only to proteins, it could be some lipid, carbohydrate, any molecule big enough. Most of the time it's some protein, but it's not an allergy proteins in general.
Do you react to other fish products such as south east Asian fish sauce? Salted and/or fermented fish?
I'd guess that your allergy is to some class of proteins in the fish - and that the production steps for dried bonito (and maybe the time required) denature or destroy those proteins.