There is no condition which causes enlargement of Adam's apple as it is a rigid cartilage and hardly any disease can occur in it. Apart from the name (
thyroid cartilage) it has no real relation with thyroid gland. You might be suffering from reflux laryngopharyngitis which is type of acidity related disorder which can present with throat irritation and swallowing difficulties
Next Steps
Consult nearby ENT specialist for confirmation of diagnosis and appropriate treatment if required