Air Purifiers

No central air or heat, so in winter windows are cracked and in summer windows are screened but opened. I bought the air purifier to help with allergies and after 2 nights it does seem to help, but think I need to go back and get the larger one. This one is for room 10 x 12 and my room is 16 x 13 and is connected to kitchen with no dividing door. Am I fighting a losing battle, or will this unit help pretty bad allergies (I think mostly to dust)? Would love to hear your experiences.
P.S. I bought the Holmes brand with Hepa type filter.
Thank you.

This is the description :

Cleaning the air in your home is easier and more stylish with the Honeywell Tower HEPA Air Purifier. The Lifetime Permanent HEPA-Type filter helps reduce up to 99% of airborne particles such as dust, pollen, cat dander, smoke and mold spores from the air that passes through the filter. Easy to clean, vacuum-able HEPA filters save you hundreds in replacement filter costs compared to replacement filter models. An electronic filter clean indicator illuminates to remind you when to clean the filter. A built-in ionizer delivers extra cleaning power and helps freshen the air that passes through it. The filter also features an antimicrobial treatment to help prevent mold growth on the filter. Ideal for medium size rooms up to 169 sq. feet (13x13) with 3 cleaning levels for quiet performance. Start enjoying cleaner, fresher air today with a sleek Honeywell HEPA-Type Tower Air Purifier for your home or office.

Permanent HEPAClean filter-never needs replacing
Helps reduce 99% of airborne particles such

It says it only fits a (13X13) room .. the room I want to use this for is a school classroom that is atleast 20X20. If i put this purifier in a spot i believe the air is at its worse, will it work for a 13X13 area from that point forward or does this product become completely useless when its in a room any larger then (13X13).

Also, i am trying to find an air purifier in the 0-0 for a larger sized room, so if you have other suggestion please list

I live in an older house (about 1100 sq. ft.). We have a terrible mold problem. I’ve been using a HEPA system, but the filters are .00 each, and it takes three of them. I’m interested in hearing from anyone who has experience with the Ionic Pro Turbo air purifier, as to how well it performs, or what is the best, affordable, air purification system.
In the meanwhile, I think I found a better solution. I bought two 20 inch, square, window fans (.85 each). Then, I bought two 20X20 3M Ultra Allergen Filterete furnace filters (.75 each), and simply put them on the back side of the fan.

Man, does it ever filter. It puts out a lot of air, and the filters catch allergenic particles such as mold, and even smoke. So far, it works great. And it sure beats paying 0, for an air purifier, (which is basically just a fan with an allergenic furnace type filter on it anyway), and .00 for replacement filters!