Usually a pain in lower back shooting down the leg is due to sciatica. Kidney stones should however be looked into since you have pain in lower abdomen. Another possibility is that along with sciatica, you have compression of the superficial peroneal nerve—this causes pain in groin area and upper thigh.
Sciatica occurs due to overuse of the lower back as in work requiring too much of bending, lifting weight, fall on the back, overweight, canal stenosis, bone disease, spondylosis, poor posture etc. Poor posture while sleeping, sitting on computers or jobs for a long time, uneven bed, exposure of back to cold air while sleeping can cause a discomfort for a few days. Take a multivitamin, plenty of fluids, and an OTC analgesic. Apply a local analgesic and apply a heating pad and see if it helps. If this does not help, consult a neurologist. A MRI of the spine and nerve conduction studies may also be needed. The treatment is to remove the compression. You have to discuss the best treatment option with a neurologist, which can range from medication to physiotherapy to traction, lumbar belts, lumbar corsets or even surgery. Hope this helps. Take care!
The medical advice given should not be considered a substitute for medical care provided by a doctor who can examine you. The advice may not be completely correct for you as the doctor cannot examine you and does not know your complete medical history. Hence this reply to your post should only be considered as a guiding line and you must consult your doctor at the earliest for your medical problem.