I am sorry about your sister.
Your sister probably has delirium
in which people often find it difficult to sleep. She needs sedatives under the guidance of your physician, because given her condition , you should not take the chance of giving anything to her on your own.
Anti-depressants are used to treat depression
, while sedatives induce sleep. They are different drug classes altogether.
It should take considerable time for her to recover since Diffuse axonal injury
is a very severe injury.
I wish you all the strength to deal with this.