What Causes Heart Palpitations, Shortness Of Breath And Weakness After Brief Exercise?

I have a health issue that I cant figure out. (it might be heart related(?)). I have no other related symptoms but these 2: after a short walk, or a brief exersize, I start to feel slightly weak , and can actually feel my heartbeat in my neck, and the pulses of blood coursing thru my veins, ......but the terrible coughing jags (that always follows afterwords!,) are very scary, and not normal for me. I have no other cold symptoms, and the coughing is not associated with a head cold, sinuitius, the flu, etc. etc. I am 67 years old,( take no pills, and have no other health problems, and have been in pretty good health till 5 months ago, when these coughing jags started,.... I figured they would go away, but as time goes by, they seem to be getting worse. My dr. has given me an x-ray, blood test, (which results were o.k.) and she doesn t seem to have any answers for my problem. Should I get a stress test? Are my ongoing coughing fits the result of blood flow problems/ or a potential heart problem indication?......... thanks for any helpful information........jerry