My daughter used to get patches like this in her early teens. They came from nowhere and like you we went through all the possibilities of what we were using, eating, etc. that might be different. I started using washing liquid instead of powder on clothes and that seemed to help a bit but didn't stop it completely. The doctor thought she was allergic to something (helpful!) so prescribed Zirtek (also available over the counter) and she took one at the first sign of the patches appearing; this also seemed to stop any reoccurence within the next day or so. She is 19 now and they stopped 2 or 3 years ago as suddenly as they started.