All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we praise you for your fear of falling into Fitnah (temptation) and ask Allah to bless you with steadfastness in obeying Him and increase you in righteousness and chastity.
There is no doubt that freely-mixed schools are an evil, an affliction, and a means of Fitnah. A person's religiosity is his most valuable possession and the worthiest of being preserved. Preserving it takes precedence over preserving all other necessities of life, let alone non-necessities. In principle, leaving this mixed school where you are not safe from Fitnah is an obligation. So you should strive to convince your parents to let you enroll in an online school. If you succeed in convincing them, all praise be to Allah; otherwise, it is impermissible for you to use your parents' identification papers without their permission.
However, since you have only a few months left to graduate from this mixed school, then consider remaining in it and only be present at school when needed, try to find good friends who help you do good, and avoid socializing with bad company. If you can do that, you would realize both benefits; finishing your studies while preserving your religiosity, and pleasing your parents.
Allah knows best.