It is possible to sue a state for malpractice, but it is not easy (you are well advised to be looking for a lawyer, and you will want to find one quickly - there are relatively short timelines to deal with when you have to work with governmental entities).
Medical malpractice claims are based on expert testimony, this means you, or your attorney, will need to find a medical expert in the same, or similar field, to testify as to the standard of care in the industry, whether your physician or facility's conduct fell below that standard, and whether that negligence was the cause of your injury. The same (or a different) expert can then testify as to your projected future damages and cost of medical care.
Due to the complexity of these claims, I highly recommend that you retain a medical malpractice plaintiff's lawyer (also called trial attorneys). Fortunately the majority of these attorneys will provide you with a free consultation, and many will represent you on a contingency basis (they will advance the costs of litigation and legal services in exchange for a portion of your successful settlement or judgment).
You can find local attorneys using the State and Local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).