Don't panic, I assume yours is a dry cough, which means you are not producing any sputum. In that case, chronic cough can be due to allergy too. There is a cough varient type of asthma which can present like this.
Next Steps
Do a total count with ESR. See if your eosinophil count is elevated. You can approach a general physician or a pulmonologist with the reports. You can also do an allergic skin test.