Yes, you could have a spinal cord injury without having any symptoms, at least at first. Adrenaline and shock are likely getting you through the initial impact of the injury, but as that wears off, you might begin noticing symptoms such as pain in the head, neck, and back. You could also feel pressure from swelling and bleeding around the spinal cord. If you suffer bone fractures in the vertebral column, you will likely feel significant pain.