What is the difference between Air Purifiers , Dehumidifiers, and a Humidifier?
What would be the best to make my room less stuffy, because my nose gets really dry to the point it hurts and I cant breath when I close my door and window. If I leave the window open I get sick. Which one would best fit me?

Hello friend, I happen to have a purifier (actually 2) in my home and I would like to help you with your choice. Let me start with the easiest ones first:
Dehumidifiers decrease the levels of humidity in your home, like its namesake. They do this essentially by drying the air, which is good for a situation like hot weather or even water damage.
A humidifier does the opposite by increasing the levels of humidity. They do this by increasing the moisture in the air. Recommended for dry weather conditions and stale air (the kind that feels like you can’t breathe in!) But do NOT use these in homes with a history of water damage – that can can actually help mold grow!
And now for air purifiers. There’s several flavors of these and various ways it can work to clean the air, and these are the ones you should buy in your situation, assuming you’ve checked your home for any leakage, and you yourself are not sick with any kind of medical condition that prevents you from opening your window…. Let me just get straight to the ones I have which clean the air through a process called "IONIZATION". Very technical.
Essentially, the dust and dirt in the air gets absorbed by the purifier and goes through a filtration process where electric currents will create and charge ions negatively in order to remove the dirt from them. From the other end of the filter the charged ions will flow out with clean air! This in turn will create more ions, and the cycle continues. It is actually similar to the way the OZONE layer work so make sure that you are not allergic to this – you’ll notice it immediate in your room by the smell it gives, which is like the ocean.
Sounds like some environmental allergens causing your problems.
Seal your house from dust. Remove dust from your environment. Air purifiers are not that helpful since those that are available to everyone have limited effectiveness. Humidity can be added to your central heating/AC system, but then you have to consider the cost of this. Dehumidifiers remove moisture from the air.
Try allergy medicines and a trip to the allergist to test for which specific items are causing your problems.
An air purifier removes solid contaminants from the air.
A humidifier adds moisture to dry air.
A dehumidifier removes moisture from damp air.