All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we congratulate you on the blessing of being safe and sound as the consequences of what happened to you could have been much worse if not for Allaah's mercy. So this is a great blessing which you should thank Allaah for day and night. Allaah says (what means): {So remember Me; I will remember you. And be grateful to Me and do not deny Me.}[Quran 2:152]
The Diyah (compensation) for injuries differs from one injury to another. Some compensations are fixed and some are not. In the absence of a predetermined compensation for injury, trustworthy experts determine the amount by using their personal discretion and considering what the injury requires. You can refer to an Islamic center or another authoritative organization which is concerned with investigating the Muslims' affairs. It is not permissible to refer to man-made law without necessity.
If this woman is mentally ill as you mentioned, then she is not accountable if she committed a sin while unconscious. The Prophet said: “The pen has been lifted from three: a sleeping person until he wakes up, a child until he reaches maturity and an insane person until he gains consciousness.” [Abu Daawood, At-Tirmithi, An-Nasaa’i and Ibn Maajah]
This does not however remove liability. The jurists have stated that if an insane person assaulted and killed someone or caused bodily injury, then his family is responsible for paying the compensation. Anything that is one third of the Diyah or less than that is to be taken from the property of the insane person if he has property. But there is a difference of opinion concerning this.
Measures should be taken to keep this woman from harming others. It is known that if you forgive her, your will be rewarded. Please refer to Fatwa 84351 about the virtues of forgiveness. The fact that you have not told your family about this incident is evidence of your good conduct and character, and you will be rewarded for this, Allaah willing. There is apparently no benefit in telling them, so you should not do so.
Dear sister, try to remove this fear from yourself and don't let it overwhelm you. Instead, frequently engage in the remembrance of Allaah, especially in the morning and evening. ‘Uthmaan Ibn ‘Affaan said: I heard the Prophet say: “Nothing will harm the person until he wakes up in the morning who says three times Bismillaahi al-lathi laa yadhurru ma‘asmihi shay’un fil-ardhi wa-laa fis-samaa’ wa-huwa As-Samee‘ Al-‘Aleem (In the Name of Allaah with whose name nothing on earth or in the heavens harms and He is the Hearing, the Knowing), and whoever says it three times in the morning nothing will harm him until the evening.” [Ahmad]
If you need to consult a psychiatrist, then do so.
Allaah Knows best.