My daughters cat did that. Hacking a lot and then being out of breath. The only way to know was take him to a vet. He was on meds for few years after vet diagnosed him. And then all of a sudden his asthma just disappeared. The vet guessed his asthma was environmental, they lived in a basement apartment which was damp and possibly moldy. He is perfectly fine now. No asthma and no coughing

You might have to take him to a vet in august to test him

I’ll PM you re vet visit