Begin by steam cleaning the carpets. If you rent a "rug doctor" type of unit go over the carpet several times. You could hier a pro, but I believe you can spend more time on the job yourself to go over the rug several times.
Next look at the furnace. In my old apartment, the furnace was improperly installed so that it sucked most of the air from around the bottom instead of through the filter. If the furnace filtering system seems to be working, then get a good $10 filter.
Finally, look around for other causes. Has it been excessively wet in your location during the last 6 months? Any molds growing in hidden places? Get a new dog or cat?
Also, for the past 4 months (June 15 to Sept 15) most states in the U.S. have required RVP (Reduced Vapor Petrolum) gasoline to be sold. This product is known to cause severe respitory problems in many individuals.
Wouldn't be the first time a government as the source of the problem. Well, vote for George W, and he will do away with this crap legislation. Or vote for Al Gore and he will make gasoline too expensive to buy. Either way it should help to breath better. Just with the latter you'll have to walk everywhere...