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Ask a doctor services. I have read your question.
You have a history of allergy. Allergy is an over reaction of the immune system to harmless substances. You had been using Budecort, a corticosteroid to get relief. Presently you are having persistent cough.
You are suggested to visit a GP, get physically examined & get sputum examination, blood workout & Imaging tests(X-Ray chest, CT, MRI, done to detect the factor causing cough.
Persistent cough can be due to allergy, asthma,
sinusitis,
bronchitis,
Pharyngitis,
laryngitis, COPD, etc. Your treatment will depend upon the pathology detected.
Since you have been diagnosed with Allergy. Your should stay away from dust, pollen, smoke, food that does not suit you. Avoid stress & anxiety for they trigger symptoms of asthma(coughing with troubled breathing).
Get evaluated & treated for the factor(pathology) causing you discomfort, you will get relieved of your symptoms.
Stay away from addictions if any. Hope I have answered your question. Take care.
Regards,
Dr Nupur K