Pyelonephritis: This condition, an infection of the kidney, often presents with flank pain (which can be perceived as backache) and systemic symptoms such as nausea and vomiting. The left-sided backache could indicate involvement of the left kidney.

Nephrolithiasis (Kidney Stones): Kidney stones can cause severe pain, often radiating to the back, and nausea or vomiting, especially if the stone is obstructing the flow of urine.
Gastroenteritis: Although primarily affecting the gastrointestinal tract, severe cases can lead to dehydration and electrolyte imbalances, potentially causing muscle cramps or back pain.
Pancreatitis: Inflammation of the pancreas can cause severe abdominal pain that radiates to the back and is often accompanied by nausea and vomiting.

Abdominal Aortic Aneurysm: A potentially life-threatening condition where the aorta enlarges and can rupture, causing severe back pain and vomiting. Although less common, it's critical to rule out due to its high mortality rate if ruptured.
Ectopic Pregnancy: In women of childbearing age, an ectopic pregnancy can cause abdominal pain, which might be perceived as backache, along with vomiting. It's a medical emergency requiring immediate attention.
Pulmonary Embolism: While more commonly associated with respiratory symptoms, a pulmonary embolism can cause sudden onset of back pain and vomiting, especially if it's large and causing hemodynamic instability.

Pheochromocytoma: A rare tumor of the adrenal gland that can cause episodic hypertension, back pain, and other systemic symptoms including nausea and vomiting.
Retroperitoneal Hemorrhage: Bleeding into the space behind the peritoneum can cause back pain and systemic symptoms like vomiting, often due to an underlying condition such as a bleeding disorder or trauma.