Is it asthma or allergies?

I'm 17 years old and on my local swim team. when i was 13/14 i started to struggle with my breathing at swim team practice. I went to a doctor and after several months of seeing various doctors and having lots of different tests and scans done they told me i had exercise induced asthma. I had asthma as a baby but grew out of it and was told that they amount of exercise i do had brought it back in its new form of EIA.

The trouble is I don't think I have asthma because I never have wheezing and I never cough.

Could I be allergic to the chlorine? When I have been in the pool for a certain amount of time (30 minutes +) I start to feel sick and get very warm. I also get this pain in my chest that makes it hurt to breath out and i hold my breath or breathe in shallow rapid breaths which makes me hyperventilate.

Is it really asthma or am I one of many that have been mis - diagnosed?