As long as you're treating the problem Mand, call it what you want. That's what's important.
I know what I went through as a kid, and as an adult I was finally diagnosed with Asthma.
However, I disagree with this: "However if I jump in and give her asthma medication, it will weaken her lungs own ability to regulate thier breathing and bronchodilation adnd she will end up dependent on asthma medication for life,"
If she is not treated appropriately--which I assume you are doing--then scarring can develop and that will make any future treatment less effective. The meds do not create dependency that way, the lungs' malfunction is already there if/when asthma fully develops. Toughing it out does not make the lungs stronger, they're not muscles. What toughing it out does accomplish is depriving the body and brain of the oxygen needed to function at their fullest capacity.
Again, I hope whatever you try does work and that it is just a seasonal thing.
I feel for both of you, having been both the kid with the cough that never goes away and the mom whose kids have had a few croupy nights.