It's hard learning to trust. I've had trust issues my whole life, so I understand.
You have to put yourself out there, though. That's part of it. Start small, don't tell them all your deepest darkest secrets right away. KWIM? Just little things. Maybe even set a timeline? Sounds crazy, but since it's been awhile since you've had a friend, try and tell her one small thing about you a week. Wait for her to share something, then the next week, you share something.
Just silly things, like a boy you think is cute. Or, a teacher that is really mean, or really nice. When you're comfortable, tell her about more serious things, like your dad. You'll know when it's time, because she'll start sharing things more and more important to her.
People can get overwhelmed if they start out by saying, "My favorite color is purple" and you respond by telling them your deepest darkest secret or your most painful. Start small. On the other hand, if she is sharing things with you that seem really important, special, or painful, you need to respond. Don't reply by laughing (even nervous laughter!) or changing the subject. A good response is, "Wow. That must have made you really ....(sad, happy, mad, etc)" That opens the door for communication and sharing feelings.
Even share with her how embarrassed you were about the teacher putting your picture up in class.
You'll do fine! Is one of them the one you were talking about a while back when she asked what your dad did? Are both the girls friends with each other already, or are you all just now getting to know each other?
Congrats!
Shelly