Sometime I feel like suffocating, after having cough, but I don't have running nose. How can I get rid off that?

See doctor... A cough associated with shortness of breath can be due to chronic bronchitis, emphysema, asthma. Shortness of breath is a serious symptom that always requires an evaluation by a doctor. You likely will need tests to determine precise etiology and initiate treatment. If your shortness of breath is severe or worsening, go to the er. This needs evaluation asap. Good luck!
See your doctor. Your symptoms may be more than an acute respiratory infection, although pertussis is a possibility. Depending on your environmental history – you may be developing a form of chronic lung disease. Please see your doctor for an evaluation; he or she will potentially order pulmonary function testing. If you have any signs of respiratory distress, feeling like you can’t breathe at all, call 911!