My son is allergic to dust mites, among other things, and I've changed all his bedding to organic wool where possible, including pillows, comforter, mattress pad (which is anti-microbial and an all natural deterrent) and 100% organic cotton sheets. Also, all natural latex mattresses and pillows are recommended, as they are hypoallergenic.
I've also bought a heavy duty purifier (which I'm selling, as I'm moving abroad, so let me know if you're interested), which measure the air quality in the room and cleans it. He turns this on every single night:
https://www.amazon.co.uk/WINIX-Purifier ... B011U6W7BM