Eliminate all carpets, first of all. They both produce and trap dust, so bad all around.

The fewer people and animals you have living with you the less skin dust and animal dander you'll have, but I assume (unless you are really dedicated to this dust-free lifestyle) that's not really negotiable.

Use as few blankets as possible, and wash the hell out of the ones you do have with fabric softener and dryer sheets. Make sure your clothes dryer vent is clean, or better yet use a dryer somewhere outside your house: they create dust.

Put your mattress into a hypoallergenic dust bag (one for controlling dust mites). Especially if it's old, it may be coughing out stuff every time you lie down on it.

After that, the next thing is probably a tie between air filtration and really frequent cleaning of all flat surfaces with a HEPA vacuum. In terms of air filters, there are a lot of threads on them if you search. Be careful of filter and electricity costs. Running your house air handling system constantly and changing the whole house filter frequently may make a difference, but it might just stir up dust until you get things really clean.

Keeping the house relatively humid can also help, but you have to be careful of mold which is IMO far worse than dust.

I have severe dust mite allergies (I'm talking serious hives on contact with a dusty surface). Here are some things I do to control it:

— Be clean as fuck. I clean all the time. It's just dust control 101. Microfiber is your friend.

— If you live somewhere with carpet, you should move out... or install hardwood floors or linoleum or anything but carpet.

— If you have any furniture with fabric, switch it out for leather or plastic or just throw it out. If you can't do either, then you need to clean the fuck out of your furniture. Get a vacuum nozzle and vacuum like crazy. Wash any removable covers.

— Cover your bed with a dust mite case. It's like a normal bed sheet except it encases your entire mattress and has a waxy inside. If you can't get a hold of one, look for a bed sheet for bedwetters. Pretty much the same thing.

— Do your laundry weekly. Including everything on your bed. If you don't have the time, the very least you should be doing is running your sheets, blankets, pillows cases, curtains through the dryer on the highest heat.

— Throw out your stuffed animals or just keep them away from you.

— Use a vacuum with a high quality filter and vacuum as often as possible (several times a week but it depends on how large your space is)

— Keep an air purifier on as often as you can. They're like reverse fans, sort of, with a filter.

— If possible, live somewhere with a central vacuum.

— Get an ionizer. This one is pretty controversial. But I'll do whatever it takes to control my allergies. Including riding on placebo effects.

In the long term, you need to move to somewhere without carpet. If it improves your health, it's worth renting a single room in a house with hardwood floors. Improved health will allow you to work more hours so you can then move back into an apartment.

In the short term, you can vacuum the carpet. I would recommend regularly renting a carpet cleaner if you can afford it. It won't get everything, but it will help. You could try splitting the cost of the rental with a neighbor as usually the rental is for 24 hours. Maybe offer to do their carpets too?

Have you got allergy covers for your pillow and mattress?