Allergies, Wheezing, Coughing, Zyrtec, Clartin, Clartin D, Grandfather Had Asthma, Mother Has Bronchitis

Every time I get allergies , I end up wheezing and coughing, even after I ve taken allergy medicines. I ve tried Zyrtec, Claritin, Claritin D , and even a cough/cold medicines (not all at once, but on completely different days). My paternal grandfather has asthma, and my mother has had many issues with bronchitis(most likely due to smoking, but not sure). Is it very likely that I have a form of asthma myself, and If so can it be tested for even if I don t have symptoms at the time. p.s. I ve only felt like I can t breathe at all one or two times, one was induced by running. However, any time I run, I tend to lose my breath very quickly