Talking to your pediatrician might help, but I might also contact your local boys & girls club or any program working with youth...they will probably have many different resources in addition to truly 'knowing' who has success in working with youth going through difficult times.
I have extensive history working with high risk youth and while the cutting is super scary, the cutting rarely is dangerous. Most of the youth I knew who cut used it as a coping tool because the sensation from the cutting made them feel emotionally better. In a way, it is her solution right now because she doesn't have any other tools that work as well...right now. You might try to express to her that she isn't crazy for cutting, many people who don't know how to handle extreme emotions turn to cutting and seeing a therapist typically helps them find other coping skills that are not only safer but work even better (infected skin can get out of control quite rapidly in some cases, which impacts the image-conscious youth even more!). It might even work to help her recognize that if she doesn't seek help in figuring out other ways of coping, she will feel crazy anyways because typically cutters keep their secret pretty well, which manifests into an even stronger belief that there is something 'wrong' with them...the cycle of shame and blame over cutting eventually feeds itself until the cutting happens to deal with the fact that the cutting is happening in the first place.
I guess what I mostly want to convey here is that you should maybe take a deep breath and try with all your might not to view her cutting as the scariest thing ever because what you think about her matters more than you will ever imagine...and if she see's you are scared of her behavior, she will probably assume you are scared of her and think it's because she's crazy or is a bad person on some level. And in order to make YOU feel better, she'll conceal her suffering and it might manifest into something much larger and scarier than cutting.
Let her know you love her and care about her and that when she's hurting, you want her to feel safe, but you also want her to feel confident and smart and beautiful and capable because you believe she is all of those wonderful things. Let her know that she is not alone and things will work out if she wants them to and asks for help. Her well-being is what matters more than anything else. There is nothing wrong with not knowing what to do, but there is something wrong with not trying to find solutions to painful challenges...let her know you believe in her and will have her back no matter how long it takes.
All of the above sentiments have been said to me by youth in similar and worse positions over the years. They want to trust their parents and they want their parents to trust them. If they think their parents don't trust them, then they don't trust their parents...if that makes sense? Provide a caring and supportive relationship and let your daughter know that while she might be afraid to see a therapist, you are her mother and love her and want to protect her, even protect her from herself. Let her know she will have a say in who she decides to stay with as far as therapists go, you will trust her judgment on this, but that the decision about seeing a therapist in general needs to be made by you at this time. This way she knows she has some control (important for her to feel safe with herself...not feeling in control leads to more cutting). If she can trust you with this, you will return trust in her judgment as time goes on about whether therapy is working or if a different therapist should be tried. Make sure she's an active participant in deciding if the therapist is working out so she has buy-in and feels like she is actually doing something, besides cutting, to help herself. Will help her confidence...and this is what you want, things that boost her confidence legitimately (complementing teens for silly things, like breathing or putting a dirty dish in the sink sets the bar low, they see right through it, and it makes them feel less competent).
I'm sorry if any of this sounds confusing...feel free to e-mail me if you have any questions or need me to clarify anything. I just felt the need to share what I know so you can start to calm down a bit, be present for your daughter instead of distracted by your fears, and so you can realize there is hope here and maybe, when all is said and done, the cutting being discovered leads to resolution of the deeper things going on that she's successfully hidden from you until this point. We don't want our kids to hide such things from us even if it's really scary to see them.
OK...sorry for long response...I'm done:)