It is possible that you have asthma or acid reflux (which can mimic the symptoms of asthma).
Chest tightness and difficulty breathing are two of the main symptoms of asthma so you should definitely see a pulmonologist right away to get your breathing tested and to get on a treatment plan. If you have any symptoms of acid reflux (heartburn, feeling of a lump in your throat, etc.) be sure to tell the doctor so that he can treat the acid reflux. If it is causing the symptoms you'll need to get it under control to manage the asthma symptoms (and for some people treating the acid reflux will cause the asthma to subside).