Air Purifiers

i have asthma and was told that a HEPA air filter would help a lot, especially since i keep two parakeets in my room and they can cause dander. so, i wanted to know how much they cost and is an air purifier the same thing? I saw air purifiers at walmart and some said that they produce hot air and other said that they produce cool air? which should i get? hot or cold? thanks!

The past people who have lived in the home I live in now did not put an air filter in the central A/C (A large square whole that sucks the hot air on the ceiling). I suspected this because when I started using it and later notice there was no filter. If thats the case, would this cause the dust to clog other vents around that goes to other rooms around the house? If so, how do I clean it out? Is it possible to do it yourself or will I need to hire someone? One of my rooms in the house does not have good ventalation and it gets hot. Also, the thermostat says "Replace Filter" even after I replace it with a brand new one.