This really caught my eye, because I had a reaction to sulfa when I was a child and so have always told the doctors that I may be allergic to it. Yet, I have used Neosporin many times with no ill effects. I had to do some research on this, and this is what I found.
Sulfa Vs. Sulfites Vs. Sulfur Allergies - Confusing Terminology
http://healthbeatnews.com/news/archives/345
To summarize the article, our allergy to sulfa drugs is not due to sulfur in the drugs; sulfur is an essential mineral that our bodies require. It's unlikely that you have an allergy to sulfates either (sulfate is found in rain water), so perhaps something else in the Neosporin is causing your allergy. It's something you might want to check further. According to the Neosporin web site, Neosporin is NOT a sulfa drug. (So what was your doctor thinking?)
I hope this helps. I certainly learned something, including that sulfa, sulfite, sulfate, and sulfur are identical to sulpha, sulphite, sulphate, sulphur.