I'm annoyed at my mum
Why are you annoyed at your mom? She is your mother.
I have a very complicated relationship with my mother
It's understandable to not always get along with your family. You should probably talk to your mother about this and tell her how you feel, especially if she's not aware she's annoying you.
I can't talk with her. It would ruin the relationship.
But how do you know that? She might actually be hoping deep down that you would reach out and talk to her. It never hurts to try; it's not like she is a stranger and will disappear.