What to do about AC and Electricity Usage?

We live in Hawaii but are originally from NC, so we’re used to hot, humid springs and summers. We’re also used to running central AC constantly. When we moved here, we turned on our central AC like we would have back home. The 1st month’s bill wasn’t too bad, but it was only for half the month. The next 2 bills shot up to 0-400. Those bills stated we were using about 1400 kwh electricity.

So, since we’re close to the beach, we have a pretty good breeze running through the house, so we opened the windows, bought some standing fans, and turned the AC completely off. We had no way whatsoever to pay a 0 utilities bill every month. So, for the most part, it works. It’s not humid like it is back home, so we’re ok. The hottest it can get in the house, on a breeze-free day, is 80-82. Right now, I’m fine and it’s probably 75ish.

The only problem I have with this setup, is the amount of dust, dirt, and hair in my house. We have a dog and cat, both who shed of course. We have grass in our small backyard so it helps the dog not to track in a lot of dirt, but my husband and our roommate track in dirt from work everyday on their combat boots (they’re in the army).

We have dark wood in our living room and within a day or two, it’s COVERED in dust. It’s insane. Same thing with the floor. There is dust, dog hair, and dirt everywhere within 2-3 days. I have to sweep and vacuum at least every 4-5 days. We’re planning on getting some area rugs, but that doesn’t make me feel any better knowing it’ll just be trapped in the carpet. We have all tile floors, bedroom and bathrooms too. I hate these floors so much. They’re stained a reddish brown b/c of the Hawaiian red mud everywhere and I’m always sweeping and vacuuming and it’s still always dirty, so I don’t even bother to scrub out the red stains anymore. It’s a nightmare of a cleaning to do and I’d have to do it several times a week.

My question is, since we have no way to run the central AC for cooling purposes since it’s so expensive, and the floor fans push the dust around so much, would it be worth it to try to set the AC to "fan only" for a little while and let it clean the air? Would it still be ok on price (Hawaii’s electric costs are 3x the mainland’s O_o) to do it? We’re on an enlisted soldier’s salary so we don’t have money to go out and buy a HEPA air filter/air purifier. And those are only for one room anyway.

We can’t close the windows and turn off the fans or we’d roast. But all this dust is triggering my husband’s migraines again and I can feel my sinuses all swollen right at this moment. Even the dog has been sneezing! I use swiffer dusters, but I’m planning on buying some Pledge cleaner this afternoon to see if it helps.

Anyway, would the "fan only" setting on the central AC work on purifying the air but in a cost efficient manner? If not, any ideas on what in the world to do until we can move out of this god-awful state and back home?