Can having carpeting in your home increase irritation for a person if you already have regular sinus/allergy issues?

Pontentially, yes: Fixed wall-to-wall carpeting can have its own problems of collecting dust and dust mites, molds underneath at times, all these add to the environmental burden in patients prone to/have allergies already. Other floorings would better with movable carpeting, if feasible, best wishes

Likely: Since one can really not clean a carpet, it is a source for dust mites, danders, insect particles, molds if you are allergic to any of these agents. Hard flooring is usually a better choice for those with allergies. A throw rug may be used on bedroom floor if one cannot tolerate a cold floor.