Thanks for your question on Healthcare Magic.
I can understand your concern. 
Yes, possibility of bronchitis is more likely.
Best treatment for bronchitis is inhaled treatment. 
Since you are not receiving inhaled treatment, you are not improving. 
So better to 
consult pulmonologist and get done PFT (Pulmonary Function Test).
PFT will tell you about severity of the disease and treatment is based on severity only. 
You will need inhaled bronchodilators (
formoterol or 
salmeterol) and inhaled corticosteroid (ICS) (
budesonide or 
fluticasone).
Don't worry, you will be alright with all these. 
No need for another antibiotic. 
Hope I have solved your query. I will be happy to help you further. Wish you good health. Thanks.