This could be a reaction to the cardboard. I know that when I prepare storage boxes at work, I have a problem with the odor of the chemicals in the cardboard and the dust. I use the plastic boards purchased from Polar Notions. It was a big initial expense, but I've used and reused them for 5 years and they are as good as new.
"So my only stash is on comic boards on a shelf out in the open."