My two cents worth are that muscle relants are contraindicated. Their use will agravate the injury. The "sprain" diagnosis is rather meaningless. Most likely you have a compression of one of the discs and loos of muscle tone will only cause further compression and mashing of the nerve. The very last thing you want to do is to lose muscle tone. What would be helpful is a TENS device, which is electrical and requires instruction by a technician or physician. A non-steroidal antiinflammatory such as Motrin is appropriate. Keep weel hydrated, avoid further strain and get a lumbar MRI.
Thank you for your question. Although without being able to examine you I can not offer you the specific advice on diagnosis and treatment that you need, but I would try to provide you some relevant information about your health concern.
It depends with situation to situation to get recovery from sprain condition. Complete recovery will be a slow process and very heavy pain-killers may be given if sprain is severe. You can also try with hot fomentation (warm cotton cloth application) on affected area and consult an orthopedician for prescription. He can examine you in person and prescribe proper pain-reliever with muscle-relaxants, if required. Hope this helps.