When you're exposed, that means you may have the spores -- the anthrax spores that they have found in nasalpassages, that they found on the computer keyboard, for example.
Also consider long-acting decongestant sprays or tablets, which help keep blocked nasalpassages open when cabin pressure changes during take-off and landing. (Decongestant can be overly drying in airplane cabin air so consider saline solution, too).