Is this wrong?

Me

A customer came into my job and aside from her complaining about having to speak to those “damn indians who don’t know english” on the phone, she was also tired of her “cotton-picking bill”. After she left I told my manager I didn’t want to help her anymore because I am tired of these comments. A coworker of mine (older white man from the south) said that I was sensitive, that’s a normal phrase, and I need to get over it. I told him if we allow these phrases that were created during slavery, we allow racism and prejudice to subliminally continue. I am tired of it. Am i being sensitive or is it normal to call a bill you’re annoyed with a “cotton-picking bill”?