Being awakened, or waking up with numbness, tingling, pain in the hands and fingers is a common sign of compression of the median nerve.
Compression of the median nerve is what causes carpal tunnel syndrome (CTS). However, due to positioning while we sleep, it is common for this nerve to be compressed, without actually having CTS.
When we sleep, we tend to bring the hands up under our chins, flexing down the wrist. Or we sleep with our hands under the chin or head, supporting the head. This causes the nerve to go to sleep, from the compression.
When we wake up, we straighten out the wrists and shake the hands, the nerve wakes up, and the symptoms go away. If the symptoms persist, then CTS may be present.
If the symptoms really bother you, you can try wearing light wrist splints while you sleep. This just keeps the wrist from being flexed down, nothing more. When the wrists are not flexed, the nerve is not compressed. This is the first thing that hand surgeons try for the night waking from CTS. If this does not help, then you would need a thorough examination of the entire upper extremity and cervical spine.
Low back injury, injury in the lumbar region, would not cause upper extremity problems. If, however, your back injury was in the neck region, then cervical spine problems can cause radiculopathy, or numbness/tingling in certain regions of the upper extremities.