Am I entitled to money since my back was hurt in a car accident that wasn't my fault?

You need to consult with a personal injury attorney about this. Every person's injuries are different. Did you go to the hospital? Were you treated by a doctor for these injuries? Did you or will you have to have an operation on your back due to these injuries? Do you have medical bills for this injury? Are you still seeing a doctor for these injuries? If you answered yes to any of these questions, please contact a personal injury attorney and discuss your case with him/her for further clarification of monetary remunification.

Have you filed a claim against the insurer of the person who was at fault?

No one is ever "entitled" to money, if you were in a car wreck that was not your fault, who was the driver that was at fault, were you treated by a doctor, how long ago was the accident. Was there a law suit, did you already settle any claim.

Not enough info to even guess at an answer

Am I entitled to money since my back was hurt in a car accident that wasn't my fault?
Where are you located, and what are your injuries?