Usually this is a CA glue allergy and the plastic cement doesn't have the same formulation. I also have a CA glue allergy. I figured it out several years ago.
Try different glues, some were worse for me than others. The gel glues caused me the least number of reactions. The thin liquids were the worst.
You can also try "foam safe" CA glues, usually found at model airplane shops or websites, and these caused me no issues, but are a little harder to work with.
But I switched to mostly plastic models to avoid the CA glues since I could use the plastic cement. When I do use CA glues, I do it on my back porch, and use the Loctite Ultra Control Gel. I got it at Home Depot, but it is pretty popular. I've found it gave me the smallest reactions.
Last edited by RealGenius; 09-13-2015 at 08:30 AM.