It got me into trouble with my friends, plus she lied to my face about it. Should I forgive her or not?
Don't share your online passwords with anyone.
Not your boyfriend, not your sister, not your friends, not even your goldfish.
Imagine if your BFF had gotten into a fight with you. She could've done way more damage with your Facebook account than just getting some people mad at you.
Now that you know the rule about passwords, here's how to clear your reputation. Log in to Facebook, change your password and send out a status update that says: "I'm sorry if you read something I said on here the other day that upset you. Someone else who was using my account said those things. I won't let it happen again." Don't name check your BFF or it'll just fan the flames.
Then, assuming your friend regrets what she did, go ahead and forgive her. Friends are allowed to make mistakes, as long as they really, truly learn from them and change their ways.