in an exposed situation like carpet (as opposed to behind dry-wall or the like), there wouldn't necessarily have to be anything you could see for the molds to be there. inside walls and at other out of the way locations, it has a good chance to get very out of hand before symptoms occur, so it leaves visual evidence, when the problem comes up quick there will be much less to see.
some are being found to have some serious health problems that come along with them. there is very little hard info on molds, even less with bacteria.
the problem with this situation of knowing there's a problem but not having any idea exactly what should be done about it (obviously it needs to be removed and cleaned, but there are no real industry standards that are universally excepted), is that it leaves a wide-open market for con-men and unscrupulous contractors. they say you have mold, and start draining your wallet. there have been a few stories going around (though nothing I've personally run into), of contractors getting positive test results, and when the owner seems less than enthusiastic about paying for mold abatement, they threaten to take test results to insurance companies, or local health code people to threaten the homeowner with condemning the property. mostly this kind of scam is pulled on hotels and apartments where the owner is threatened with loss of income if regulatory agencies deem their property unsafe to occupy.
with the molds there is a realization of problems but only a few that have been cataloged and accepted as 'known dangers', as of last summer (my last training update) there were little or no standards set for exposer levels or much in the way of hard figures at all. most of the research is originally done as to how it affects occupational health and safety standards, so I wouldn't expect a lot of new info any time soon.
you can get test kits for the more common molds (though I don't know where you'd purchase them for retail sale), just a treated swab that you rub on the suspected area and send in for results.
I'd reconsider running your central air though, if it does turn out to be a mold problem, you are running a good chance of having to de-con your duct work. I'd use rental de-humidifiers and fans, maybe even price a HEPA filter unit to clean the air, all rentals that you can rent, clean, and take away from your home when finished.
since your problem came on fairly quickly it shouldn't be too extensive, mostly just removal of the effected material.
if you do decide to remove it yourself I might be able to be of some help.
>standard disclaimer>>> I couldn't give actual advice for your situation(since I'm not there, covered by insurance, or licensed in your state). but I could discus, hypothetically, what sort of personal protection a person who had found themselves in your situation might want to take while handling the mess.