Most Helpful Girl
If you felt you had to tell her it's fine. But it's a little harsh to me. She wished you happy birthday, it's not a big deal... You could leave it there. It's up to you. :)
Most Helpful Guy
Here is the great thing about breaking up, you are no longer responsible for how she feels. Her emotions are no concern to you.
It doesn't matter if what you did was harsh or not, the fact is she doesn't make you happy when she talks to you, so you told her to quit. Now you'll be happier and you can make others happier in turn.
She isn't a part of your life, so don't sweat it.