I had terribly allergic rhinitis throughout my youth, but only at my family's home. When, after I moved out, my parents pulled out the carpet in my old bedroom, my allergies at that house vanished.
I use low-cost area rugs which get shaken outside regularly or simply replaced.
I've nailed a few heavy-duty spring-loaded clamps to an elevated wood deck joist where I hang them for shaking and a day in the sun every couple weeks. Don't even have a vacuum cleaner anymore, it's a huge improvement in quality of life.