I did the same thing. I would recommend not pushing her on anything in specific, like her being withdrawn. Just try to spend extra time with her, be extra accommodating, and a little extra loving. Not overwhelmingly so... just invite her along a lot. Like, find to time to say, "Hey, would you like to go to get our nails done today?" Or if money is an issue just, "Would you want to go to the mall with me? Would you like to make a cake? Want to invite a friend over tonight?" You get the idea, I'm sure. And if you're both bad at baking.. that just makes the cake thing way more fun. Haha.
Really. She might just be suffering from depression. Lots of teenagers do. School is a terribly hard social environment and then add in the hormonal changes, the dealing with coming into her own, and everything. Don't be overly anything with her. If you seem too worried, hurt, angry, annoyed, or too ANYTHING... she will feel overwhelmed. The best advice I can give is try to include her and spend time with her, but always be very chilled out. It will help her relax a little.
If you are aggressive about this... she will resent you for it. And she will only want to push you away. DO NOT FORCE YOURSELF INTO THIS. Teenagers, especially edgy or depressed ones, do not respond well at all to forceful or demanding behavior. And about the don't let her go anywhere unless you're there??? That will make her crazy. She's 13. She needs her independence. Don't get overly worked up or scared. She just needs a little extra love, one on one time, and support. She'll most likely open up to you if you are consistent. Even if she pushes you away at first and declines your invitations, she will come around.
You also might want to think about treating her to special alone time. Like, set her up with bath salts, some candles, a good books she'd like, maybe even a fruit tray in the bathroom. Just give her an hour or two to pamper herself by herself. Every girl needs a good pampering! If you did that maybe once every two weeks, it could help her nerves a lot.
Plus, the poems are a good thing. It's helping her vent and express herself.
I wish you the best of luck and please let us know how it goes!!!