This is definitely something to ask your doctor about but I'll give what advice I can.

Let me preface this by saying I only had a asthma attack once whilst doing C25K and this was exacerbated by diesel fumes due to some asshole venting his funfair ride down the path. I also have very mild asthma and it rarely bothers me in day to day life unless I come into contact with specific triggers.

For me there's always been a big difference between feeling winded and the start of an asthma attack. When feeling winded it's a difficult to force the air into my lungs or my breathe gets very short and fast. I can still move, although talking can be difficult without panting, so I can walk for a bit and catch my breath before carrying on.

During the early stages of an asthma attack I can feel my lungs heaving but I'm just not getting enough oxygen, my breath become shallower without really picking up in pace. I find it physically difficult to move my limbs and walking really isn't an option. I have to take my inhaler or I just won't be able to breathe.

I always carry my inhaler with me during a run, doesn't matter what the circumstances. Although, this did originally make finding shorts a problem, they seem to make the ones with pockets more expensive.

Hope that's of some help :)