My chest and throat feel itchy almost painful. And I have a bad cough what could this be?

Throat and chest. Frequently, itching is a symptom of an allergy. Post nasal drip from the nose or sinuses can lead to irritated throat and cough. Asthma can present as a recurrent cough and asthma is frequently associated with allergies. An evaluation could include lung function testing, allergy testing and possibly sinus ct scan.