You know what? You've got a friend who wants to be supportive of you, and is probably worried about you. Count yourself very lucky!

Are you trying to protect yourself from being hurt? I mean are you worried that you will rely on her too much and she'll go away?

Please remember that not talking about what is wrong will only contribute to you wanting to self-injure more. If you have someone who wants to be supportive of you, let her be! That's a wonderful thing to have!

I think you messed up a little by telling her nothing was wrong, but that's not a huge deal. It's definitely forgivable. I DON'T think you did the wrong thing by admitting to her that you lied. I personally think you should tell her WHY you lied about it. Maybe even show her this post. Lying to your friends is NOT cool, and it's a darn good way to chase them away. Don't chase this one away. She's there for you!

Best of luck to you, and your friend
Angela