It sounds like it was just an impulse. While that impulse needs to be addressed I don't think you need to give up your university career and move back home; unless you feel like that is the best option for you.

I will be happy to give you a story that the German ER will accept to treat your wrist wounds without a psychiatric evaluation. If you are not in a good mental state right now that might not be the best thing to do right now.

If the wounds are not something that needs to be stitched, you can go out in long sleeves and buy antibacterial ointment, gauze and medical tape.

Apply the ointment to the wound, then wrap it in the sterile gauze. Don't do it tightly but just enough so that it protects the wound.

In the mean time I think you should talk to the embassy about finding mental health services in English. I know they have them near the major American military bases. If you are in a remote part of Germany it might be slightly more difficult.