Keep suggesting that she see someone. It isn't a matter of being insane or not and she needs to understand that mental health is as important as physical health and is not something to be ashamed of or frightened about. Obviously what has happened has concerned her enough to tell you because she recognizes and admits that all is not the way it should be. I would say that fear is what is holding her back so you need to reassure her any way you can that seeking professional help is for her own well being. The suicide and self harm may be gone for now but may come back without warning as well so do not lower your guard in that respect. As a way of weaning her into the idea of getting help why don't you set her up on the computer to do some of the online quizzes and tests. Do them together with her in a light hearted way so that she doesn't feel like a target. Some of those results may reveal some finer details about her behavior and make her aware of her own feelings. They may also be beneficial to you as her friend to know how her mind is thinking etc. In the meantime keep doing what your doing and be particularly mindful of subtle changes in her behavior and don't let your guard down with regard to potential self harm.