During your interview you will be given the chance to explain why you are seeking protection by the German state. If you can provide convincing evidence for why your life is in danger, why you have to fear persecution in your home country (e.g. for religious reasons) or other factors that might play a role in your case, you will be granted protection.
I can't tell you if injuries are enough proof because I don't know how exactly BAMF comes to their conclusions. But you should definitely tell them about it.
In most cases it makes sense to consult a local counselling center for refugees before the interview. They can take a look at your case in depth and give you tips for the interview.