Is the questioner's situation considered a case of necessity, permitting her to travel without a mahram, given her poor psychological and familial state, her suicide attempts, and the absence of any relatives to support her?

Suicide is one of the gravest sins and a sign of a bad ending. The one who commits suicide will be tormented in the afterlife with that by which he killed himself. Whoever contemplates it must repent to Allah and increase in good deeds, for the torment of the Hereafter cannot be compared to the torment of this world, and patience in calamities is rewarded immensely. As for a woman traveling without a mahram, it is not permissible except in cases of extreme necessity that cannot be averted otherwise, while preserving her religion and honor.