Yes. If you suffered an injury due to your physician's negligence, you could sue to recover economic and non-economic damages. Economic damages include medical bills, lost time from work, and home care costs. Non-economic damages include pain and suffering, psychological trauma, and lost quality of life.
As in anesthesia malpractice, to successfully sue after a failed back surgery, you will need to present proof of duty, breach, causation, and damages. Your personal injury lawyer will hire a surgeon specializing in back surgeries to testify that your physician failed to conform to the standard of care.