How Quickly Does Prednisone Work--?

For years now--whenever I get any kind of cold--or allergy reaction--or a Sinus flare- I develop a dry cough that lingers for days (Or sometimes a couple weeks )

Awhile back--I went to an excellent Pulmonary Specialist (She was very thorough ) & was tested for asthma (neg) & even "Cough Variant asthma) Negative also !

She said--I have "Hypersensitive Bronchial tubes"--!

Anyway--last week--had some really bad issues w sinuses (post nasal drip) inflamed throat--Well- that is all gone- but this darn--dry- persistent cough continues (OTC cough meds only offer temporary relief)-

So my E/N/T Dr--just prescribed a 5 day regimen ..of Prednisone (40 mg--after meals--once/day)

Any of you here--helped by this ?? (I just took my first dose at 1 PM --EDT) -I understand it helps w inflammation --

If so---- about...how long...before I start feeling--at least some relief from this cough..??

Hoping to hear-- Any positive feedback will help--(Never took Prednisone before)-
This is not a heavy dose--is it..?

Thanks,
Rob