Your "lumbar spine," or low back, is made up of five bones that are placed on top of each other and separated by a shock-absorbing disc. Your low back's muscles and ligaments provide a great deal of support. "Sprains" and "strains" are a direct result of these tissues being stretched too hard or too far, much in the same way that a rope frays when it is stretched beyond its normal capacity.
A "sprain" is when the thick, strong ligaments that hold your bones are damaged, but a "strain" is when the muscles or tendons that move your trunk are partially ruptured.
Bed rest is not in your best interest, and you should only allow yourself to return to normal activities as your symptoms allow.
A lumbar support belt might help reduce your discomfort for a short period of time. Sitting raises the risk of back sprains or sprains induced by sudden movements. It may be wise to take "micro-breaks" from workstations for 10 seconds every 20 minutes. After an acute injury, apply ice for 15-20 minutes every hour. Heat may also be helpful after several days or for more chronic origins of pain. Be sure to inform your doctor of your exact situation and to ask for specific ice/heat recommendations. Sports creams have provided partial alleviation for some people.