Most acute back pain gets better with a few weeks of home treatment. Over-the-counter pain relievers and the use of heat or ice might be all you need. Bed rest isn't recommended.
Continue your activities as much as you can tolerate. Try light activity, such as walking and activities of daily living. Stop activity that increases pain, but don't avoid activity out of fear of pain. If home treatments aren't working after several weeks...if no improvements consult your doctor might suggest stronger medications or other therapies.