Persistent cough, no pain, red throat, kinda itchy. japan dry air?

Allergies: You are describing what sounds like allergies with post-nasal drip. You could try a non-drowsy antihistamine such as fexofenadine or loratadine, and/or a cortisone nasal spray such as fluticasone or triamcinolone. These will reduce your itchiness, and reduce your cough if cause by PND. See your doctor to make sure you don't have asthma.