I'm not licensed in AL, so I'll give you some general information. In general, an employee can bring a workers' comp claim if he/she is injured at work. It's called a "claim" rather than a suit. Most states require employees to be able to point to a certain time when they were injured. By that I mean the general time of the day and what they were doing when they felt pain. The exception to this is occupational disease or repetitive motion claims. There is also usually a requirement that that the employer be notified of the injury within a time period set by statute. There is also a statute of limitation for filing the claim.
You should definitely contact an AL workers' comp attorney about your claim ASAP. I'm sure that he/she will be happy to speak with you since your injury is obviously very serious. Good luck!
You might be able to sue them, but it depends on what occurred. Did your employer have notice that you were injured on the job? If so, did they pay for the treatment and surgery? You have two years from the date of the incident in which to file suit regardless of whether you are still employed with them or not.