I had inconclusive testing with all but one of my lung tests. The total lung volume test they did (me sitting in this airtight booth thing and panting) came up with air trapping. Other than that I was "normal". While my peak flow readings were 250-310 at the doctor's office before and during testing and now at home it is around 400-420 and I had reached 440 on really good days. Hmmm something wrong there? I think so.
I started with advair (corticosteroid and long acting broncodilator) which worked but very expensive ($120 every 2 weeks) so we switched to pulmicort that is only a corticosteroid. It took about 2 weeks to notice any difference until that inflammation went down, it is only now that the albuterol (rescue inhaler) makes a difference.
You also have the same symptoms as me. I would get another opinion if you don't think the diagnosis is correct.
Yes, I do believe that you should see another doctor; a lung specialist, also called a pulmonologist. Lung disease or heart disease could be the cause of your cough, chest tightness and shortness of breath. It is most important that the correct diagnosis be made, without further delay. Despite the poor response to inhaled medicine, the correct diagnosis could still be asthma, worsened by air pollution, even with normal pulmonary function tests (PFTs). But that diagnosis should not be assumed.
You could have other, more serious lung disease, even with only a possibly normal or slightly abnormal chest x-ray. For example you could have pulmonary hypertension (PH), recurrent pulmonary emboli (PE) commonly called blood clots with or without PH, bronchiolitis alluded to in the interpretation of your chest x-ray as “small airways looked pronounced” and any one of a variety of lung diseases classified as interstitial lung disease (ILD). And there are other, much less common causes such as lymphangioleiomyomatosis (LAM) that would need to be considered.
Unless you can be proven to have asthma with the improvement one expects to see with medicine, your condition warrants further investigation, beginning with consultation with the lung specialist, followed by a high resolution CT scan of your lungs.
One final thought. You mentioned that you have mitral valve prolapse (MVP). The vast majority of people with MVP are asymptomatic and remain so throughout their lives but the disease is characterized by a wide range of symptoms and functional impairment. Your doctors may want to reevaluate the MVP, before assuming that the problem definitely resides within your lungs.