An Absolute Eosinophil Count of 680 is mildly elevated and, along with a persistent cough, may be related to Eosinophilia, allergies, asthma, sinus disease, parasitic infection, reflux, or other lung conditions. Since medicines like Monticope A, Allegra, Laveta M, and Hetrazan have not helped, further evaluation is important rather than continuing self-medication. A physician or pulmonologist may advise tests such as chest X-ray/CT, spirometry, IgE levels, allergy testing, stool tests, or evaluation for asthma and sinus disease. Please seek medical follow-up, especially if you develop wheezing, breathing difficulty, weight loss, or fever.