Do you think it is normal for me to hate this super nice girl at work who has done nothing to deserve my hatred?
What has she done to make you hate her?
She slept with my ex.
I'm sorry she did that to you.  You don't have to like her, but you should make an effort to get along with her at least since she's your coworker.  You don't want to cause drama at the office!
It's not like she's the reason my ex left me.
Exactly, you need to stay positive and try keeping it civil with this co-worker. That seems like a very positive way to look at it.