Thanks for your question.

You're up against one of the most difficult situations in the sense of trying to help someone who appears not to want it. As a 14 year old I think it isn't unreasonable to anticipate a level of anxiety that may ebb and flow. The issue with any therapy is that the client has to feel a relationship with the therapist and actually want the therapy.

CBT is educative and does require a conceptual grasp which, perhaps, your daughter feels unable to accept at this stage. Although CBT is generally regarded as one of the most effective forms of therapy for anxiety there are others, such as one-to-one counseling she might feel happier with.

It may not always feel this way but a significant issue for her will be the fact that she can turn to someone who provides unconditional love and support. Of course you will want to suggest things and offer direction but unless and until she is ready to accept a therapeutic relationship it can't be imposed. 

Meanwhile I suggest you/she look at the things known to affect arousal states. These include the pattern of sleep, diet, restricting high sugary intake of foods and drinks, and getting regular exercise.