I've Had A Cough The Past 9 Days. Within The

I've had a cough the past 9 days. Within the past 5 it's been very congested and has had mucus, and in the past 2 it has effected my asthma, causing it to be very difficult to breath during terrible coughing fits. I went to the doctor 6 days ago and was told I had allergy and asthma caused bronchitis. Then was perscribed a steroid pack and cough medicine that I have since then finished. Should I have gotten better by now?