Most patients with thyroid cancer do not have any symptoms. Typically, patients present with a thyroid nodule that is found to be cancer on further evaluation. As with all thyroid disease, a thorough history is important, such as a family history of thyroid cancer, personal history of radiation exposure, or enlarged lymph nodes. Your physician will review with you any symptoms such as pain, swelling in the neck, difficulty with swallowing, shortness of breath, difficulty with breathing or changes in your voice. If the nodule is large, it may cause symptoms such as difficulty swallowing, choking sensations, or a large mass in the neck. Rarely, the cancer can grow into the nerves (i.e. the recurrent laryngeal nerves) that control the voicebox and cause hoarseness.
For more information go the endocrinediseases.org:
Diseases of thyroid gland: Thyroid cancer