Why do I get sick sleeping next to fake wood furniture?

Formaldehyde? Off-gassing of formaldehyde from new pressed wood furniture or wood paneling can trigger irritant respiratory symptoms. If you have asthma, formaldehyde can trigger an asthma attack. The mechanism is inhalation of a respiratory irritant not an allergen. It might be possible to seal the furniture with polyurethane. Make sure to do this in a well-ventilated spot & allow ample time for drying.