Good point. After re-reading the original post I see that the symptoms were still present the next day. This would be unusual if it was caused by asthma. At least in my experience.
Although I don't know if this is true for everyone my symptoms which include wheezing and dificulty in getting enough air on each breath begins to diminish soon after I terminate the activity. On those occasions where I have gone on a run in cold weather and forgotten my inhaler I have managed to reduce the symptoms simply by slowing the pace.
In general my asthma is well controlled with medication so I don't experience symptoms unless I forget to take my meds or am under unusal stress (stress is another trigger for asthma along with alergens).
I guess its possible that the problem is EIA but only a professional could say for sure.
Randy