If you have seasonal allergies, any time you expose yourself to the allergen outdoors, you will probably make your symptoms worse. In a car, the air that comes in is from the outside, and is often not filtered completely. Thus, it would not surprise me if your symptoms of seasonal allergies were not helped by keeping the windows up in your car. You may have to experiment to find out.
I will say that many people with bad seasonal allergies do tend to spend more time indoors in the air conditioning. Many people buy air conditioner filters which are specially made to filter out the pollen and other plant like material that causes seasonal allergies.
While trying to avoid the allergens is always a good idea, I would also urge you to seek treatment that will prevent your allergy symptoms from occurring in the first place. There are many options that can be tried. For example, your doctor
can prescribe you a steroid nasal spray which can prevent your allergy symptoms from occurring when you get exposed to the allergen. In addition, you can get a prescription for an antihistamine medication that can help treat your symptoms when you do get them. You should schedule an appointment with your primary care physician
for this treatment.