Anonymous wrote:OP here. Thanks all. I don't think the carpet is the main culprit, although we have plans to get rid of that anyway. The only room with carpeting is our bedroom, and oddly enough, that's one of the rooms I have the fewest issues being in. I'm intrigued by the mold idea (the first PP give me hope!) and would be interested to hear from anyone who may have had similar issues where mold ended up being the culprit.
Mold can also lurk behind the walls so if a good solid duct cleaning doesn't do the trick you might want to consider checking your walls. If you live in a TH your neighbors might have a mold problem on the shared wall.