No, this is not pleurisy. Pleurisy is chest pain that occurs with breathing.
I can’t speculate what is going on with the limited information you have provided, but I am not convinced, regarding your shortness of breath, that cardiac disease and asthma have been ruled out as the cause.
Your having trouble breathing for a month is worrisome. The cause of this must be determined with reasonable certainty, if appropriate treatment is to begin. You may want to consider requesting a second opinion.