I agree with sealing your house and making it 'air tight'. The less unfiltered air coming into your house the better. AC's help to filter the air as it comes in and definitely keep up with changing the air filters (or cleaning them if washable...just make sure you use soap and water when cleaning and not just water).
I have asthma and had attacks every other day when I first moved to this state. I recommend going to an asthma specialist (Pulmonary Doctor) to get your asthma under control through medication. There are plants that grow in North Texas and no where else on this planet. These plants wreck havoc on asthmatics and are most likely mixed in with the dust around your house.
I do not agree with using a humidifier though. During the summer here the humidity outside is already high and I'm sure inside the humidity is at a reasonable level already. You can use one at night but only in your bedroom and only while you sleep. I'm also thinking that if you use a humidifier all the time you'll be creating (if not adding) mold and mildew to your house and black mold is a major health hazard here.
Using a humidifier during the winter is highly recommended though. The winter weather tends to be dry so adding moisture to the air will not only add warmth, but it'll alleviate having dry skin.