I'm going to stop talking to a girl when she was depressed because it was making me depressed
How is she making you depressed?
Talking to her upsets me.
Depression hits everyone differently, some people are comfortable talking about it while others are not. Rather than ignoring her when she needs you, try to listen to what she's saying and encourage her to get help.
I'm just too busy to help her today.
Well you should consider how she feels, I'm sure she likes talking to you and it makes her feel better. You shouldn't just abandon her.