Nephrolithiasis (Kidney Stones): Given the patient's history of kidney stones, severe abdominal and back pain, nausea, and vomiting are classic symptoms of a kidney stone, especially if it is obstructing the ureter. The fact that the CT scan is normal does not entirely rule out a small stone or a stone that is not radiopaque.

Pyelonephritis or Urinary Tract Infection (UTI): Severe abdominal and back pain, along with nausea and vomiting, can be symptoms of an upper urinary tract infection. The normal CT scan does not rule out this diagnosis, as it is typically diagnosed through urinalysis and culture.
Gastroenteritis: Although the primary complaint is abdominal and back pain, gastroenteritis can cause severe nausea, vomiting, and abdominal pain. The back pain could be referred or due to the intense abdominal cramping.
Pancreatitis: This condition can cause severe abdominal pain that radiates to the back, along with nausea and vomiting. A normal CT scan might not show pancreatitis if it's early or mild, but elevated pancreatic enzymes would be diagnostic.

Ectopic Pregnancy: Although less likely given the patient's symptoms and the fact that a pregnancy test is not mentioned, an ectopic pregnancy can cause severe abdominal and back pain, nausea, and vomiting. It's a life-threatening condition that must be considered, especially in women of childbearing age.
Appendicitis: While the pain pattern is not typical for appendicitis (usually starts around the navel and then moves to the lower right abdomen), atypical presentations can occur, especially in women. Appendicitis can cause nausea, vomiting, and severe abdominal pain.
Ovarian Torsion: This is a gynecological emergency that can cause severe, sudden onset of abdominal pain, nausea, and vomiting. It might not be directly visible on a CT scan unless there's associated ovarian edema or other secondary signs.

Porphyria: A group of disorders that can cause severe abdominal pain, nausea, vomiting, and neurological symptoms. It's rare but should be considered in cases of unexplained severe abdominal pain.
Lead Poisoning: Can cause abdominal pain, nausea, vomiting, and constipation, among other symptoms. It's less likely but could be considered if there's a history of exposure.
Intestinal Obstruction: Although the CT scan is normal, early or partial obstruction might not be visible. Symptoms can include severe abdominal pain, nausea, vomiting, and obstipation.