Back injuries by nurses are common...I have several such cases/clients right now. You can file a WC claim against your former employer, but the employer/insurer will almost certainly deny the claim if you didn't report it to anyone while you still worked there. Call your former supervisor and say you need to report a workers' comp claim; then ask for the panel of physicians.
Yes, you do have a claim for workers' compensation if your doctor has connected your work-related duties to your current medical condition. I would be curious as to what he diagnosed you with, i.e. degenerative disc disease, herniated disc, etc. The strength of your case can sometimes turn on what you have. In some cases, such as carpal tunnel, the date of injury may not be until the point where your doctor has taken you out of work. This is called a cumulative trauma injury. If that were the case, you would have 30 days to notify your supervisor. This sounds like that type of case, so you should consult with an experienced workers' compensation attorney to discuss your options. Also, notice to your supervisor can be subtle. It doesn't have to be "hey boss, my back hurts, and it was caused by my job duties, and now I have a workers' compensation claim. Best of health - feel better soon!
You can definitely file a workers' compensatoin case aginst your prior employer. Just remember that you will need to file a claim with the State Board of Workers' Compensaton within one year of the date of injury.