Thank you for clarifying the matter.
In general, it is possible to have a second job.
But as an asylum seeker you have to ask Ausländerbehörde for permission for every single job that you want to do.
In addition you might have to talk to your employer at Pflegeheim first. Take a look at your work contract to find out what you have to do exactly. If it doesn't say anything about Nebenjob you don't have to tell your employer. If it does contain a paragraph about Nebenjobs you either a) have to tell him about it or b) ask him for permission. As I said, check the contract for details.