Generally, it would irritate your whole/at least part of the respiratory tract.
Your lungs are constantly exposed to danger from the dusts we breathe. Luckily, the lungs have another function - they have defense mechanisms that protects them by removing dust particles from the respiratory system. However, that does not mean you should be enjoying living in a dusty room. Even though the lungs can clear themselves, excessive inhalation of dust may result in disease. If the dust particles settle in the nose, it may lead lead to an upper respiratory tract disorder called rhinitis. It can also cause tracheitis (inflammation of the trachea) or the bronchitis (inflammation of the bronchi).
Amount of dust? Well, I guess you live an area where there is a lot of dust. The wind is probably causing the dusts to enter through the window.
I guess you should try cleaning your house everyday (don't know if that's practical, sorry!)