Serious family issues, Depression, intense desire to have sex and suicidal threats shows she has serious emotional problems. Her pressure on you may be a part of her dependence and deep down desire of being wanted. Sometimes depressed person may have increased desire to have a sex. You should not succumb to her pressure if you really do not wish to get into it. Another possibility is, she may develop physical attachment to you once you enter in to sexual relationship with her. I think you should stay away from her.