Can deet make your skin peel?

Bought some bug spray that’s 23% deet. Really need it because I’m going to be spending June and July in deep woods. I’ve used it a couple of times and my arms are now peeling a little bit. I’ve not heard of this happening, but I can’t really think of another reason why my arms would be peely – haven’t gotten a sunburn, skin doesn’t seem to be dry, etc.

Should I stop using it?