That depends on what you did to hurt your back. Blunt force trauma could result local bruising or even caused a pulmonary contusion (bruise of the lung). Depending on the severity of back injury, trauma may also result in fractured ribs.
Treatments for uncomplicated back pain include resting, icing, and NSAIDs (ibuprofen, acetamenophen, etc.). You should be concerned if you have shortness of breath, you feel an obvious boney deformity, the pain doesn’t resolve, or the pain worsens. Then, you may need to be evaluated by a doctor with a physical exam or xray imaging.