Some species of Ringworm (but not all) will show up under UV light. Some people call the light a 'Woods Lamp' and all vets should have one lurking in the back of a cupboard. A lighting technician would call it a black light. The infected area will glow like white does under a UV light in a nightclub. It can be confirmed by a skin scrape sent to a lab.
I'd say from what you've now told us you need to mention to your vet that it's highly likely your house has been exposed to Ringworm. I could well be wrong here as still only going on hunches and not much evidence but now you've said that it IS worth a serious consideration.
It's also worth having a good inspection of yourselves (don't forget to look in your hair!) for the tell-tale patches. Ringworm is one of the very few things that can jump from humans to animals and back again. It can be treated but you must follow rigid instructions and it takes many weeks to clear up.
To give you an idea on how persistant Ringworm can be, it's CP policy that wooden frame cat pens that have been exposed to Ringworm carriers have to be burnt as they must never be used again. It is not possible to sterilise due to the way Ringworm spores burrow down into wood.