Have pneumonia asthma bronchitis on prednisone 40mgx5 levoflaxcin500x7 is ok to take benedryl, cough supp and expectorant to manage severe coughing?

Probably OK but.. If your cough is caused by uncontrolled asthma, then you need to get the asthma under control instead of relying on cough medicine to relieve the symptoms. On the other hand, if your lung function is reasonably good and the cough is too bothersome, i see no harm in taking a cough suppressant for a few days. I would suggest that you talk to your doctor about these issues.