Unknown causes: cough

I've been to see many doctor's In this month...
I went to see my ENT doctor because I have been coughing for a few days even though I don't have soar throat or fever. I don't cough at night and at motion. I have cough up phlegm, too. So I might have asthma or bronchitis, so I visited him.
I found out unknown causes. He said I should see my physician at the internal medicine after taking meds for a week if my cough continues with meds.
After taking meds for a few days, I started coughing once at night as well. The next day, I coughed again before my alarm clock rang. I think I need to see my physician this Saturday, but I don't have my family doctor recently. He closed his own clinic year ago due to his old age. Now he is employed and works at a large hospital. So I want to go to pulmonary department nearby, but it is very famous and need a reservation. It will take 2 months to see him!
Or I can see a good doctor after driving 1.5 hours. Well it will see.