The nerve most likely injured in this patient is the left recurrent laryngeal nerve. The left recurrent laryngeal nerve, which is a branch of the vagus nerve (cranial nerve X), and is responsible for innervating the muscles of the larynx that contribute to moving the vocal folds. Therefore, if there is an injury to the left recurrent laryngeal nerve, the laryngeal muscles will be affected, weakening movement of the vocal folds, and causing a hoarse voice and difficulty swallowing, as is present in this patient. 

The facial nerve is responsible for a number of functions including facial movements and taste, but not voice or swallowing.

The long thoracic nerve innervates the serratus anterior muscle. When injured, this can result in a "winged scapula," but not voice or swallowing changes. 

The trigeminal nerve is responsible for a number of functions including chewing, biting, and facial sensation, but not voice or swallowing.

There is no such nerve as the "esophageal nerve."

The cavernous sinus is unique in which it uses the superior petrosal sinus to drain into the transverse sagittal sinus. Whereas, the straight, superior sagittal sinus, and cerebellar sinus all drain into the confluence of sinuses. Then the confluence of sinuses later drains into the transverse sagittal sinus as well.

The right pulmonary vein supplies blood to the left atrium.

The internal iliac artery is responsible for a number of branches including:the iliolumbar, lateral sacral, superior gluteal, obturator, inferior gluteal, umbilical, uterine, vaginal, inferior vesical, middle rectal, and internal pudendal arteries. 

The duodenum receives arterial blood from two sources, the celiac trunk and the superior mesenteric artery.  The proximal duodenum is supplied by the gastroduodenal artery and its branch the superior pancreaticoduodenal artery. Both of these branches are supplied by the celiac trunk. The distal duodenum (midgut) is supplied by the superior mesenteric artery and its branch, the inferior pancreaticoduodenal artery. Although the superior and inferior pancreaticoduodenal arteries have different sources they form an anastomatic loop between the celiac trunk and superior mesenteric artery.

The superior mesenteric artery arises off the anterior surface of the abdominal artery just inferior to the celiac trunk (around L1). The superior mesenteric artery (and its branches) supplies the intestine from the distal duodenum to the proximal two thirds of the transverse colon. It also supplies the pancreas.

The intercostal space is the space between two ribs. As there are 12 ribs on each side, there are 11 intercostal spaces which are numbered for the rib superior to it. Within the intercostal space there are muscles, lymph nodes, nerves, arteries and veins. The vein, artery, and nerve (in this order) run together in the neurovascular bundle within the intercostal space. The neurovascular bundle runs directly inferior to the rib.

The celiac trunk is a major branch of the abdominal aorta. The celiac trunk has three main branches (each of which has its own branches), which include: the left gastric artery, the common hepatic artery, and the splenic artery. 

The splenic artery provides blood supply to the spleen. The colon is supplied by the superior mesenteric, inferior mesenteric, and the iliac arteries (the superior and inferior mesenteric arteries are other major branches off the abdominal aorta). The appendix is supplied by the appendicular artery, and the jejunum is supplied by the superior mesenteric artery.

A dermatome is an area of skin that is supplied by a single spinal nerve. There are eight cervical nerves, 12 thoracic nerves, 5 lumbar nerves, and 5 sacral nerves. Each of these nerves is responsible for sending sensation from a particular area of the skin to the brain. Frequently tested dermatomes include T4 (the level of the nipple), T10 (the level of the umbilicus), and S4/S5 (the perianal area).

The intercostal space is the space between two ribs. As there are 12 ribs on each side, there are 11 intercostal spaces which are numbered for the rib superior to it. Within the intercostal space there are muscles, lymph nodes, nerves, arteries and veins. Within the intercostal space the vein, artery, and nerve (in this order) run together in the neurovascular bundle. The neurovascular bundle runs directly inferior to the rib.

Knowing the relationship of the neurovascular bundle is important clinically. When performing a procedure called a thoracocentesis (inserting a chest tube) one needs to avoid damaging the neurovascular bundle. Thus when performing procedures one inserts the instrument directly above the upper margin of the rib.