Thank you for writing. I’m appreciating the situation you find yourself in. On the one hand, you want to be helpful to your student. On the other hand, as a new teacher you don’t want to unintentionally step outside of school policy by approaching her directly.
You didn’t mention if you followed up with the pastoral care teacher. If not, that would be the first step. It would also be wise to talk with your supervisor about policy around what the school sees as appropriate boundaries between teachers and students. Does the school support teachers taking an interest in a student who seems unhappy? What are considered professional limits? What resources are available to both you and the student?
I hope there is a way for you to approach your student. Often young people don’t feel they can talk to a parent or relative about their problems. Research has shown that being able to talk to a trusted adult is often a turning point for a teen struggling with emotional issues.
I wish you well.