Can I say that I am annoyed by my cousin these days?
Oh your cousin? Seriously? Why are you annoyed with your cousin?
She always asks me to take care of her when she's in a bad mood.
While it can be frustrating dealing with someone who is not in a good mood, you should try to take care of family members. It's normal to be more patient with family members than you would be with strangers. You should do your best to help your cousin when she needs it.
Nahh! Your wrong.
Everyone is in a bad mood at one time or another. Her asking you to take care of her then is somewhat unusual but it is also nice of you to help her too. Taking care of relatives at least for a little while has it's benefits for both people, be kind to others.