Hello
You have given a good history here although there are a few things to know
1.Are you a smoker?
2.Do you have bodyache, fever, night sweats, weight loss for the past months?
The overall impression I derive is of a long standing sinus infection with a associated tonsillitis due to allergic cause. That is the reason the IgE levels are also very high for you.
The chest xray picture and your cough symptoms are indicative of Allergic bronchitis but since in our Indian setting long standing cough can also point towards tuberculosis so I advise get a tuberculosis testing done.
You need a proper nasal evaluation and few tests
Next Steps
Consultation
Health Tips
Kindly do not have over the counter medications for cough or other issues.
It will just delay your diagnosis and proper treatment.