Thanks for your question on Health Care Magic.
I can understand your concern.
Yes, you should definitely concern for these throat symptoms.
Most common cause for acute exacerbation of
asthma (acute worsening) is infection.
So we need to treat infection along with taking rescue inhaler for complete recovery.
Since you are not taking any antibiotic (fir infection), you are not improving fully.
Your throat symptoms are mostly due to infection.. So better to
consult doctor and get done clinical examination of respiratory system and start broad spectrum antibiotic like
levofloxacin or
azithromycin. It should be taken once daily for 5 days.
Don't worry, you will be alright.
Hope I have solved your query. I will be happy to help you further. Wish you good health. Thanks.