Do doctors see a lot of patients with thyroiditis?

Depends on type. Hashimotos thyroiditis or chronic thyroiditis is the most common cause of hypothyroidism and is very common. Acute thyroiditis is less common, often (but not always) painful, and temporarily increases thyroid hormone levels.
Not realy. Thyroiditis is the inflammation of the thyroid gland. The thyroid gland is located on the front of the neck below the laryngeal prominence, and makes hormones that control metabolism.