Urgent advice for toddler

Hi all. My daughter is 2.5 nearly 3. We caught covid the first week of June this year and she fully recovered within days with no symptoms left. She then had to have a minor surgery exactly one month later.

She got sick with a cold/flu two weeks after that in July and has had a chronic and persistent cough since then, even when she isn’t sick. Although she has been sick again a few times since then also. The cough has not disappeared.

I’ve had an x ray done of her chest and lungs 4-6 weeks ago all was clear.

Despite that I have no answers for this cough and I’m beyond worried at this point as it’s still here.

I need answers and want answers. Even just answers of what I could have a doctor look for.

We live with my parents and they do smoke. However it’s NEVER around her. I feel like I needed to add that in just incase. I need answers please.