Thank you for reaching out to the Wefugees community!
Whether you are allowed to be self-employed and register your own business will be dependent on certain criteria, as length of stay in Germany, if I am not mistaken. Did you check your “Aufenthaltsgestattung”? Usually it contains a note similar to “Selbstständigkeit gestattet” oder “Selbstständigkeit NICHT gestattet”.
However, please also keep in mind that being self-employed in Germany is a real challenge and requires good administrative skills and knowledge of the bureaucratic system. I think these are often underestimated factors.
I found an interesting website which gives many information on this topic.
I will also link two of our experts here. Dear @manrhei-mbeon or @mbeon-Ruth, can you maybe give some more details on this?
All the best,