Musculoskeletal strain: Given the patient's occupation as a head chef, which likely involves heavy lifting, bending, and twisting, musculoskeletal strain is a plausible cause for her back pain, especially with the pain worsening upon turning the torso, standing up, or lying on the right side.

Kidney stones (nephrolithiasis): The location of the pain (right flank/mid back) and its radiation down the right lower limb could suggest a kidney stone, although the absence of nausea, vomiting, and fever makes this less likely.
Pyelonephritis or urinary tract infection: Although the patient denies fever, chills, and genital symptoms, a urinary tract infection cannot be ruled out entirely, especially if the patient has uncontrolled hypertension, which could affect kidney function.
Herniated disk or lumbar radiculopathy: The radiation of pain down the right lower limb suggests possible nerve root involvement, which could be due to a herniated disk.

Abdominal aortic aneurysm (AAA): Although less common in women, an AAA can present with back pain and is a medical emergency. The patient's uncontrolled hypertension increases her risk.
Pulmonary embolism: While the patient does not report typical symptoms like shortness of breath or chest pain, pulmonary embolism can occasionally present with back pain and is a potentially life-threatening condition.
Spinal infection (osteomyelitis, discitis): Infections of the spine can present with back pain and are critical to diagnose early to prevent serious complications.

Pheochromocytoma: A rare tumor of the adrenal gland that can cause hypertension and episodic back pain, among other symptoms.
Primary or metastatic tumors of the spine: Although rare, tumors can cause back pain and should be considered, especially if there's a history of cancer or if the pain is persistent and unexplained by other causes.