When Lili gets nappy rash that's usually about all she gets, and it's not teething related (sorry! though you never know ), it just seems to be down to her being in a dirty or too-wet nappy for too long without me noticing (these days she usually tells me when she's had a "yucky poo" but if she doesn't feel like being changed she sometimes keeps quiet about it!).
I don't think minkee is quite as stay-dry as fleece - I'd say keep an eye on the tooth, but also try going back to fleece for a bit and see if that makes an instant difference. I don't think it's a reaction to the material per se, but it might be down to just that bit more moisture being held in. In that case, you might find they're OK for daytime use but not nights.