Can your epiglottis be swollen for 4 weeks and the only symptom be not be able to eat solid food?

Not likely: A swollen epiglottis would cause difficulty breathing because it blocks the airway. It would not typically cause problems eating solid food. Much more common reasons for trouble swallowing solid food include anxiety, muscle coordination problems, and a feeling of swelling in the throat from gastroesophageal reflux.

Epiglottitis: Epiglottitis is a condition where the flap that comers the trachea swells. This can be a life threatening condition due to the possibility of air movement being cut off. There are different causes of epiglottitis including infections, burns, and trauma. You need to be evaluated by an ENT doctor right away.