H.W.
I looked online and apparently, there was some concern with the 'tagless' Carters items... apparently, the chemical in the 'tagging' (an iron-on of some sort or print-on, maybe ) cause a recall a few years ago. Note that I only found this on the Carters site so there might be some other implications, but I'd Google it.
The other thing-- are you using flushable wipes instead of toilet paper? The soap on some of those could cause irritation.
Formaldehyde is something that causes rashes, so do some research to make sure the underwear wasn't treated with that (to stay wrinkle free) or washed with sheets which have been treated with formaldehyde. Some people have very strong rash reactions to formaldehyde.
If you do a couple laundry loads of the undies with just hot water and nothing else, see if it disappears or still continues. That will let you know what to do about them.