When my kid was diagnosed, we did the following:
1. Encased mattresses.
2. Removed area rug in bedroom.
3. Got air purifier.
4. Dusted and vacuumed bedroom more consistently.
That (and Allegra, daily during the winter) seemed to be enough to keep things under control. She does bring her own pillow if she's traveling to places like a cabin (where pillows and linens may be ancient). She also avoids sitting in old upholstered chairs/couches when we visit people. (Our own furniture doesn't seem to be a problem.)