The same type of exposure sensitivity can happen with the components that make polyurethane. Hives, dermatitis, breathing issues, flu like symptoms, etc. on related exposure (vapor or skin contact) to isocyanates or even polyols. This can be a permanent sensitivity. I would treat your sensitivity the same way, as the reaction is similar (cyanoacrylate also has highly reactive monomers) and can be cause permanent sensitivity.
In a prior life I pumped millions of pounds of single and plural component poly…. Now even a whiff or skin contact of canned “great stuff” foam curing or Gorilla wood glue is enough to cause me discomfort. I don’t get hives anymore, or at least haven’t had that large of an exposure in decades to test the theory.