A sulfate (or sulphate, same thing different spelling) is not the same as a sulfa drug. Neosporin contains Neomycin Sulfate; it could be that your reaction is to this specific sulfate, or to something else in the Neosporin. There are several active ingredients in Neosporin.
Foods never have sulfa drugs added; they have sulfites added. It's so confusing! But it is important, I think, to figure out the differences, and to pinpoint just what is causing your allergy, so that you know what to steer clear of. Telling a doctor that you have a sulfa allergy, for instance, does not tell him that you are allergic to neosporin sulfate, or that you can't tolerate sulfites in foods. Perhaps a visit to a good allergist is in order.