Please don't worry. 'Prominent bronchovascular markings' is a very common, non-specific finding on chest X-rays, often indicating mild airway inflammation or congestion rather than anything serious. Since your cough has lasted two months, we need to identify the exact underlying cause, such as post-nasal drip, cough-variant asthma, or acid reflux, before starting targeted medication. For temporary relief, you can try over-the-counter cough suppressants like dextromethorphan or antihistamines if you suspect allergies. However, to properly resolve the cough, please consult a doctor who can perform a physical exam and prescribe appropriate treatment, which may include inhaled bronchodilators like albuterol if indicated.