Why does my eosinophil count increase when the season changes?

Hi doctor,

I am a 39 year old female. My eosinophil count increase during when the season changes. From the past month, I am having a persistent cough, which is not allowing me to talk. Phlegm is also present. I have taken two bottles of cough syrup Zeet, Sensiclav 625, Montek LC, Rinifol, twice a day for five days, and Mucus cough syrup. By the time I finished taking the medicines, my cough had almost disappeared. But it returned after stopping the medicines. So, I got a blood test done, in which, my erythrocyte count was 5.38, hemoglobin was 13.9, PCV was 43.2, MCV was 80.3, neutrophils were 59.1, eosinophils were 6.1, lymphocytes were 26.8, monocytes were 7.3, and basophils were 0.7. I am taking Banocide forte from the past 10 days, but still, I did not get any relief. I am allergic to dust, and I have a dandruff problem. Please advise.

Thank you doctor,

Will these medicines or cough syrup cause sleepiness? As I am a working lady, it will be difficult to work if I am sleepy.