My daughter had this issue around the age of 15-16. The different part of my story is that she is the sister of the one with CF. My daughter is now 20 and unfortunately I did have to seek professional help with her, as we found a suicide letter half under her bed and half out. She had low self esteem. However, you would NEVER know this as she was always bubbly and outgoing and giggly when she was around that age. I call it "The Eddie Haskell" syndrome. Just a term I came up with for people that act like they are fine with a very persuasive and overly bubbly personality and then when you leave the room, they turn into a different person around different people. My daughter got caught up with the wrong people too which led her even deeper into things that she felt very ashamed of later and it was literally eating her up inside. We have always had an open door policy in our family. Me being the Dad and my Wife as well. We have always told our kids, it doesn't matter what it is, drugs, suicidal thoughts, depression, if you want to vent, boyfriend or girlfriend problems our door is always open. I even went so far as to tell them that they would never get in trouble as long as they came to me if they needed help. Not once did she ever come to us (my wife and I). But my wife and I got hit with 6 big bombs with my daughter in one single day. Here I thought I had a happy daughter and independent a thrive for life, next weekend she was writing a suicide letter and then it all came out, the drugs, the alcohol, the sex, the sneaking out, the giving all of her money away to help her friends out (car maintenance, gas, food, clothes), and the cutting. I was in utter shock.
Just be glad that you know now before something bad really happens. Be supportive and just let them know that you will always be there. I had to admit my daughter after she could not guarantee that she would NOT hurt herself landed herself in a 10 day stay in a rehab type hospital. She stated she had smoked pot (not gonna argue with this part as I did the same thing at her age, but of course you never encourage it) BUT she drove her mother's car right afterwards. The drug test came back negative and she flat out told us that she did smoke pot. We both laughed when she said with tears in her eyes "I can't even do that right".
All I can really offer for advise is stay the course, this time will pass. It is a bit cry for help and the fact that she has CF it might be more of a "I am tired of dealing with this" type of thing. If its that, I won't say don't worry because us as parents we will still worry a bit. Just try not to make a huge fuss, this will pass and she will realize that her problems really weren't as bad as she thought. It just takes time. You do still need to get help for her, because if she is cutting be darned sure that she is doing other things that you don't know about as well.
Just to lift your spirits up a bit, my daughter is 20 now. She is a manager of a store and going to college. She has decided to move out to get her own apartment, and although stressful at times she feels really happy about things now. She has come far and she is closer to her brothers (ages 17 and 16) now than when she lived with us. She loves to come over and just hangout and do things with them. She misses them and most of all, she misses my wife and I and really appreciates the things we did for her, how we didn't just ignore her when she needed us the most.