Cough restarted after prednisolone

Hi,
I have not got hebrew fonts but you can reply in hebrew - thanks.
I've had a cough for last 6 months, went to a pulmonologist,
had chest CT which showed ' minimal scarring at the lungs bases' which is according to the doctor
was jus a sign of an old infection. I had a peak flow test which was around 340 and the pulmonologist concluded that I did not have
asthma.
I then was referred to ENT who prescribed prednisolone 20mg x12 days,
I stopped coughing when took prednisolone, but after I finished, the cough gradually came back.
I saw the ENT today and he suggested that if the cough stopped and then started again it's likely
that I have a bronchial hypersensitivity,i.e. asthma? Is that so?
Thanks