Nobody else than a Doctor can Diagnose this for you. When your child has breathing issues go and see the Gp directly.

I would have him checked out by your GP. If he is diagnosed with asthma, he will also be given a treatment plan.

My daughter was constantly getting bronchilitis and other respiratory illness and we always struggled with her breathing during winter and spring and getting this viral infections.
Dry persistent cough a little cold like just a snotty nose would set her coughing off.
Then it started happening when it was. Colder of a night or morning and so on.
The dr called it at the age of 2 as there was also family history of asthma as well she’s now 5 and been on a preventive ever since.