Caregiver has it right- pleurisy itself isn't contagious, but whatever is causing it could be. Double check whatever caused it to make sure you're not putting yourself or others at risk.
Pleurisy is an inflammation of tissues around the lung, and in general, there is not much chance of contagion. Pleurisy is not necessarily inside the lung, but usually affects the sliding surfaces that surround the lungs. Thus, aerosolization of the infectious agent through coughing is not usually an issue. Bear in mind that the inflammation may, in some cases, result from tuberculosis. In such a case there is danger of contagion. The important factor is the nature of the biological agent causing the inflammation. For a certain answer consult the infectious disease specialist treating you or your loved one.
my stepdad had pleurisy, its inflammation of the lungs and chest, his was caused by pneumonia but no its not contagious