I need help with diagnosing my wife's bedroom allergies! Could it be the cedar closets in our new home?

Probably dust mite. Dust mite is the most common allergen in the bedroom. They live in your pillow, mattress, and bed linens and eat your dead skin. An allergy evaluation with a board certified allergist would be helpful in identifying the problem.
Possible. May be the cedar, or something else - consider allergy testing. This can be done by allergist or your family physician.