You should definitely see a doctor and ask about the possibility of asthma. You can have asthma even without a family history of it, especially if there is any history of any type of allergies.
Take care and feel better.
Hi, welcome to forum, your symptoms are generalized and needs a more detailed evaluation. The symptom you are having is known as dyspnea (difficulty in breathing on exertion). The possibilities are Bronchospasm (bronchial asthma), pulmonary embolism, Pneumothorax and chronic bronchitis (This seen commonly in chronic smokers) and even cardiac causes like Congestive heart failure and Cardiac tamponade can cause breathing problem but seems unlikely. Even generalized condition like anemia can also cause such symptoms.
You need to undergo pulmonary function tests like spirometry and ECG to rule out the cause. You also need to undergo ESR and certain serological tests to rule out autoimmune disorder including complete blood counts. It is difficult to come to a certain diagnosis with available history. Further evaluation is needed. I suggest you to consult physician. Take care and regards.