Afternoon, tis me, Mouse
Sorry to skip straight back to this but PURPLE, I don't think that your DD is self harming, nor is she going to. I don't think she'd kill herself either because there's no way that she'd let you see her stripped off if so. She'd hide every inch of her skin. My DD was careless when I saw her..... she'd reached up to get something and I saw her cuts across her stomach.
She's also cut chunks of her hair out from underneath thinking I wouldn't see but I did and do. I know because I was once 12,13 14..... She forgets that I was once her age.
The note could have been a test, to see if you'd say anything to her upon finding it. I don't think it's a cry for help as such or on it's own if you see what I mean, more a 'this is how I feel today, my life is super shit just now and I wish it wasn't........'
DD and I have been dancing this merry little dance of for a number of years now. Like you, I have always tried to give the her the best of things, labels that her friends were wearing when she went through that particular phase etc, when she wanted to get the same as her friends, I did all I could to make it happen. Especially before DH and I met.
She has incredibly huge lows and is often dreadfully sad which I think she has inherited that trait from me. She will wish herself dead one hour and not the next. I hated being her age, I ran away from home, all the way to the end of the road, I shit you not.
I was tired of my mother saying no to me for everything, or so I thought at that age, so I packed a bag and waited at the end of the road until my mother came home from getting my brother from school and told her I was leaving. Why the actual fuck I waited to tell her I don't know to this day!
She asked if I wanted her to ask the neighbour to drop me somewhere or was I getting the bus, did I have any money. When I said I didn't know, she suggested that I get in the house before I got cold, took my small bag out of my hand, and sent me to my room.
She said that when my father got home, she'd tell him and he'd deal with me 
He told me that in actual fact, I'd scared my mum half to death, worried her so much that she was at the kitchen table sobbing, my sister had been packed off to our aunts for dinner, and my brother was in the living room crying because mum was crying.
She was asking herself where she'd gone wrong, what she'd done to me to make me want to leave.
As mothers in particular, we have a dreadfully hard time of horMENTALS kicking in with our daughters. Or can do. Whatever 'this' is Purps, it's not you. It's no that you've failed her, let her down, not done what was best for her etc. It's just teen girls and boys can get as bad.
It's because those are words she wanted to write right there and right then, and maybe has no idea why herself. Or because she was going to show a friend at school. Or because she felt shitty that day.
Has your DD started her periods yet? I find with DD that mid-cycle she has a dreadful slump, she'll stay in bed for the day if not at school.....she really gets low and will avoid the rest of the world if she can.
She hates her life, me, DH, Nemo, her 'friends' etc on a regular basis when she's due a period.... she picks up on things very quickly, she can read situations even though I think that I've hidden them from her so well......................
I always ask if she wants to talk and except her answer unless I think she's lying, in which case I will make time, real time, to come back and ask her again.
DD's said she wanted to kill herself because of what other girls have said or done too........ I wouldn't go back to that part of my life or hers for anything.
Keep talking to her (sorry if I'm way off base with the above btw) xx