Cars can be a real irritant to people with allergies.
Wash the floor mats regularly, and make sure they are completely dry before putting them back in the car, to stop mould from forming. Vinyl seat covers are better than cloth for keeping dust and mould away from the seat upholstery. Whenever possible, travel in an air-conditioned car, so you can keep the windows closed. In spring and fall, when the air is full of allergens like pollens, keep the windows and air vents closed and recirculate the interior air. If your car is not air conditioned, cover the vents with cheesecloth, to help filter out these allergens.