Welcome to the Wefugees Community and thank you for your question.
If you are holding an "Aufenthaltsgestattung" (during the asylum procedure) or a "Duldung" (after a rejection) you have to apply at the authorities (usually the immigration office/Ausländerbehörde) if you want to move to another place than the municipality you are supposed to stay. For this, as far as I know, you have to submit a so-called "Umverteilungsantrag" in which you give good reasons/proof for your request. I believe that this process usually takes quite long and I have my doubts that you manage it within the next few weeks.
Maybe it is an option to continue school until you finished the process successfully? Maybe you can also find an "Ausbildung" (apprenticeship) without moving?
I highly recommend you to discuss your individual situation and your options at a so-called "Jugendmigrationsdienst (JMD)" office in your area. The social workers are specialised on this type of questions/topics and can support you.
Please let us know if you need help in finding such an office or if you have any further questions.
All the best,