Anyone know anything about having an inflamed trachea?

Don’t worry, I’m not substituting this for doctor’s advice.

This is NOT a COVID19 Q.

I had a cough for almost three months following an illness. I’ve taken antibiotics. My lungs are perfect on X-ray, and they feel normal again (thankfully) except for what I would say is my trachea, and possibly near where the trachea branches off into the lungs. Also, I get winded easily if I exert myself, but otherwise I feel normally oxygenated just sitting or walking around the house.

I can’t tell if it’s inflamed, or still lined with some phlegm (gross sorry).

The doctor prescribed me prednisone, but I’m afraid to take it, but still might. Sometimes I have a constant rumble/gurgle in my chest.

I’ve been thinking instead of drinking hot liquids I should maybe eat very cold things like ice cream? To reduce inflammation? Does that sound right?

I have never had a lung issue before, so I have no experience, and interested in the experience of others, don’t worry I will not take it as advice.

If it doesn’t resolve I’ll see another doctor, maybe a specialist.