I sent a really mean unprofessional email to a nosy coworker after her daughter died
Why did you send the mean email, if you knew it was unprofessional?
I wasn't thinking, I was too angry.
I understand that you were angry, but sending cruel emails to co-workers is wrong. Apologize to your co-worker and promise that it will never happen again.
I guess she just wanted to talk since she had no one to talk too.
I'm glad that you are starting to understand your coworker's intentions, and why it was wrong for you to react in anger.  Apologizing is a necessary step for you at this point.  Your coworker might not be ready to listen, and probably won't want to talk, but at least she'll know that you didn't mean to cause more harm.