I'm have asthma, and in winter if I don't start taking my preventer get a cough mainly at night just like you describe, two out of three of my kids have it and my youngest looks like she does too. With my first the dr said I think she has asthma try using the ventolin and if it makes difference let him know, it did so he started her on a preventer. My second was diagnosed at 3 months old same way. However they re checked after both their second birthdays.

I would definetly get it checked.