Thank you for your post.
From your description it shows that there is a amelioration. You should expect acute bronchitis
to last upto a couple of weeks, not more than a month. Your treatment did not include any antibiotics. Generally, acute bronchitis is caused by viruses but can also be as a result of bacteria. If the bronchitis persist within a couple of days, I'll suggest to visit his pediatrician
. Antibiotics may need to be started.
Hope this helps