Who is the racist? Are we too sensitive sometimes?

Today my landlord told me to separate the trash. Is she racist?

I am living in a shared flat with a German girl and a Polish guy. Since there's only one trash can in the house so i don't know who mixed the trash. And the landlord noticed it and came to talk to me telling me that I have to separate the trash. She also said that she would tell the other flatmates but then she said the girl is from Germany so she should know. For a moment I was pissed as I thought about if she implied that I mixed the rubbish. So I was about to show her the little bag of bio trash in my room and tell her that i'm not born yesterday and Germany is not the only country in the world doing recycle. 

But then I realized that when i'm having this thought, am i discriminating her ? Having a prejudice that she is mean and racist because she is an old German lady?

Lately I also watched a Youtube video about 'stop giving evil characters brown skin'

Which is very reasonable. But somehow the concept of "black represent evil" was there in Asia many years before they ever see a black person. Is it also racism ?