Teething can certainly give a nasty diaper rash. And yes, zinc is definitely the way to go. It creates a good barrier to protect the skin and let it heal.
From your discription, it sounds like yeast might be a possibility. Does the rash seem really painful, or not? If it is not really painful, then it might be a yeast infection rash. My girls got those when they teethed too. (not the same as our yeast infections, thank goodness!) Anyways, my doctor recommended that I use the same cream as for a vaginal yeast infection, just apply it to the rash area. Cleared it up in a couple of days!
Oh, and don't worry about the bad mummy bit - when they're teething, I think the rash happens INSTANTLY! Their poo just seems to peel the skin right off their little bums. Poor kids!