Should i be concern and see a doctor when i felt a pop and a sharp pain in and around my right diaphragm? now everytime i cough i feel that sharp pain?

If you had been coughing a lot before that happened you might have some injury to the chest wall structure such as rib or costochondral joint, not the diaphragm. You can elicit the pain by pressing the anterior aspect of the thorax along the ribs. The problem is self limited even with a broken rib. Take Tylenol or Ibuprofen + apply warm or cold pad locally.