Thanks for posting your query.
You are most likely suffering from chest infection
such as pneumonia
Presence of chest pain
along with sputum suggests the diagnosis.
Enlarged papillae on the back of tongue is enlarged lymphoid tissue also known as adenoids.
These adenoids are natural phenomenon to prevent the infection by engulfing microorganisms.
You should consult with internal medicine specialist and should go for chest x ray as a preliminary investigation.
You should also go for sputum examination.
You should also stop smoking to prevent further worsening.
You should also take proper treatment on written prescription from your treating doctor.
Dr. Mayank Bhargava