**Core Concept**
Hemorrhage is a potential complication following thyroidectomy due to the rich vascular supply of the thyroid gland. The risk of hemorrhage is increased by factors such as bleeding diathesis, anticoagulant therapy, and surgical technique.

**Why the Correct Answer is Right**
The most likely resulting complication in this scenario is hematoma formation, which occurs when bleeding from the surgical site accumulates in the neck. This can lead to compression of the trachea, esophagus, and other vital structures, potentially causing respiratory or gastrointestinal obstruction. The risk of hematoma is increased by the patient's recent surgery, which has compromised the integrity of the blood vessels in the neck.

**Why Each Wrong Option is Incorrect**
* **Option A:** Carotid artery injury is a possible complication of thyroidectomy, but it is less likely than hematoma formation. Carotid artery injury would typically present with more severe symptoms, such as severe neck pain, difficulty swallowing, and neurological deficits.
* **Option B:** Recurrent laryngeal nerve injury is a potential complication of thyroidectomy, but it would typically present with hoarseness of voice or difficulty speaking, rather than swelling in the neck.
* **Option C:** Hypocalcemia is a potential complication of thyroidectomy, but it would typically present with symptoms such as numbness or tingling in the mouth or fingers, rather than swelling in the neck.

**Clinical Pearl / High-Yield Fact**
The "hard sign" of hematoma formation is a firm, pulsatile mass in the neck, which is often accompanied by signs of airway obstruction, such as stridor or shortness of breath.

**Correct Answer:** D. Hematoma