N.W.
You can be allergic to anything, including natural products. Just because something is organic or non-toxic does not make it hypoallergenic.
I applaud you for trying to choose a "green" product. You might want to go to the product's website and contact them about your problem. Ask them for a list of "ingredients" used in the diaper, which may help you in pinpointing and avoiding whatever your daughter is allergic to.