Transfusion-Related Acute Lung Injury (TRALI): This is a leading cause of transfusion-related mortality. It occurs when transfused blood components contain antibodies against the recipient's leukocytes, leading to a severe inflammatory response in the lungs, resulting in non-cardiogenic pulmonary edema. The symptoms of hypotension and difficulty breathing shortly after a blood transfusion make TRALI a highly plausible diagnosis.

Anaphylactic Reaction: An allergic reaction to the blood transfusion can cause hypotension and respiratory distress. Although less common than TRALI, anaphylaxis is a significant consideration due to its potential for severe consequences.
Hemolytic Transfusion Reaction: This occurs when there is an incompatibility between the blood type of the donor and the recipient, leading to the destruction of red blood cells. Symptoms can include hypotension, difficulty breathing, and potentially life-threatening complications.
Fluid Overload: Especially in patients with pre-existing heart conditions, rapid infusion of blood products can lead to volume overload, resulting in pulmonary edema and symptoms of heart failure, including difficulty breathing and hypotension.

Pulmonary Embolism: Although less directly related to the transfusion process itself, a pulmonary embolism could present with sudden onset of difficulty breathing and hypotension. Given its high mortality rate if untreated, it's crucial not to miss this diagnosis.
Cardiac Tamponade: If the transfusion process or the patient's underlying condition leads to cardiac tamponade, the patient could present with hypotension and difficulty breathing. This is a medical emergency requiring immediate intervention.
Sepsis: In rare cases, transfused blood products could be contaminated, leading to sepsis. Early recognition and treatment of sepsis are critical to prevent high mortality rates.

Air Embolism: Although rare, air embolism can occur during blood transfusion, especially if there is a breach in the transfusion line or improper handling of blood products. Symptoms can include sudden onset of hypotension and respiratory distress.
Citrate Toxicity: Citrate is used as an anticoagulant in blood products. In rare cases, especially with massive transfusions, citrate toxicity can occur, leading to hypotension among other symptoms due to its effects on calcium levels and coagulation.