Thank you for clarifying the issue.
Have you read this thread about asylum based on medical reasons? https://www.wefugees.de/k/questions/1974
Here is a short summary: The medical state on its own is not sufficient to get asylum based on it. However, it is possible to get a medical report that can be handed in at Ausländerbehörde. They might take it into account and give you a Duldung. But you will have to give convincing reasons why it's necessary for you to be treated in Germany and not in your home country. I'm not sure if this works with diabetes though.
On the other hand, of course you can go through a regular asylum procedure in order to obtain asylum/residence permit.