I am in Florida, so the law is going to differ somewhat, but I would guess there are similar or parallel laws in our states. I can only answer from a Florida law standpoint, but you may find it helpful and instructive for your situation in Tennessee.
Your sister's actions are what make it difficult to get an injunction/restraining order because they know what the lines are and they walk up to it and don't cross it.
Her criminal history can certainly come into play if you have other actions and verbal communication that can be connected with her violent past history. However, her history alone is not going to be enough to make your case.
You mentioned that she was texting you to the point you had to block her. Were her texts threatening or harrassing (either by content or excessive amounts)? We have criminal statutes in Florida against harrassing phone calls and assault. Assault must be a threat of bodily harm that is immediate in nature with an apparent ability to do so. You will have a hard time with that if its done by phone.
However, given the fact that she knows where you live and work, she knows your family, that increases your risk of exposure to harm. If you can tie in her past actions/criminal history and/or if there's been any verbal threats or acts toward you at all and her current actions, then you have a better chance of obtaining an injunction. In Florida we have a couple of types of injunctions that are sought for protection: repeat violence or domestic violence. Since you are family because you are related by blood, it doesn't necessitate a prior violent act, but you do need to have a current act that would qualify as an act of domestic violence OR you must have "reasonable cause to believe" that you are in "imminent danger of becoming the victim of any act of domestic violence."
Your factual scenario will have to fit what the law requires a showing of in order to meet your burden of proof to satisfy the Court that an injunction (a/k/a restraining order) should be granted. The facts of your particular case will dictate what the Court will do. There may be many other relevant facts in your case that would be enough for a basis to grant an injunction. I don't know enough from your one-paragraph description. I would search the internet to find out what Tennessee law requires for a domestic violence injunction.
A potentially better option for you may be to seek a mental health "involuntary commitment" for your sister if such a thing exists in Tennessee. In Florida, we have a body of law called the "Baker Act." In certain cases, a person can be involuntarily committed for a mental health evaluation when they have a mental illness (which you sister has already been diagnosed) and they are in emminent danger of harming themselves or someone else. In many instances, the process begins by police who are called to the scene of an incident where it is reasonable for them to believe the above two elements are present. They take the person into custody to transport them to the facility in the area that is designated for Baker Act intakes. The other scenario in Florida is that you can file an "ex parte" petition with the court to seek the involuntary committment of a person who has a mental illness and is in danger of harming themselves or others for the purpose of having that person assessed by mental health professionals to determine the risk of harm and illness. The ex parte petition method may be your best avenue for help for your sister and protection for you and other family members. It will all depend on what facts are involved in your and your sister's situation.
I recommend contacting the Clerk of Court in your area to see what possibilites for relief exist in your state. In Florida, the clerk's offices have a person or persons (or office) that are exclusively dedicated to injunctions and petitions for other relief (ex parte petitions for the Baker Act).