Splenetic Injury or Rupture: This condition could explain the left-sided abdominal hematoma and potentially the hiccups if there's associated diaphragmatic irritation. The cough might be unrelated or a sign of an underlying condition that led to the injury.

Pneumonia or Lower Respiratory Infection: Could cause cough and potentially hiccups if there's significant irritation of the diaphragm. The abdominal hematoma might be unrelated or due to a traumatic event that also led to the infection.
Gastrointestinal Bleeding: Although less directly related to hiccups and cough, a significant GI bleed could lead to a hematoma if it tracks to the abdominal wall. The hiccups could be a sign of irritation of the diaphragm by blood in the peritoneal cavity.
Trauma: Direct trauma to the abdomen could cause a hematoma and potentially lead to hiccups and cough if there's associated injury to the chest or diaphragm.

Aortic Dissection: Although rare, an aortic dissection could present with a wide range of symptoms including abdominal pain (potentially leading to a hematoma if there's retroperitoneal bleeding), cough (if the dissection involves the ascending aorta), and hiccups (due to diaphragmatic irritation). This condition is life-threatening and requires immediate intervention.
Pulmonary Embolism: Could cause cough and potentially lead to hiccups if there's significant respiratory distress. The abdominal hematoma might be unrelated, but the combination of symptoms warrants consideration of this potentially fatal condition.
Diaphragmatic Rupture: This could cause hiccups due to diaphragmatic irritation and potentially lead to a cough. An abdominal hematoma could be present if there's associated abdominal trauma.

Neurological Conditions (e.g., Multiple Sclerosis, Stroke): Certain neurological conditions can cause hiccups. While less likely, if there's an associated cough and abdominal hematoma, it could be due to a complex interplay of symptoms or unrelated conditions.
Intra-abdominal Shunt or Fistula: Rare conditions that could potentially cause a combination of these symptoms, especially if there's a connection between the gastrointestinal tract and another system (like the respiratory system) that leads to cough and hiccups.
Tumor or Cancer: A tumor in the abdomen or chest could cause a variety of symptoms including a cough, hiccups, and potentially an abdominal hematoma if the tumor erodes into a vessel or causes significant bleeding.