Probably Ativan or Xanax. Has she been to a clinical psychologist yet? Therapy may be a better alternative, at least until the therapist recommends medication.
Her pediatrician will know the kind of medication to treat her with. While rls offered up two options, both Ativan and Xanax are pretty potent benzodeazepines and there are some that are much milder. Depending on what, (or IF) her doctor decides about medication, make sure you understand fully the pros and cons of his choice. There are long term benzos and short term benzos. Xanax is an example of a short term benzo. It is prescribed for use of not more than 4 months. Klonopin is a long term benzo and people can stay on it for years. But some meds are not recommended for kids under 18 years. All benzos carry risks and you need to talk very frankly with the doctor about those risks. While medication WILL relieve her symptoms, be aware that all they are doing is masking the underlying problem. (Which is being manifested by these very symptoms) Age appropriate therapy will help her get to the root cause of her anxiety will be taught how to overcome it. A cure is better than a bandage. Medication as an adjunct to therapy is, in my opinion, the best way to help your daughter.
Your daughter is very lucky to have a parent who believes this is not just some teenage hormonal problem or all in her head.
Would that 50 years MY parents had believed ME.
I concur with the others. When I was first diagnosed with Generalized Anxiety Disorder, my doc explained that medication is only meant to put the user into a frame of mind where they can be receptive and productively work at therapy to address the root causes.
Your daughter may need medication, but in general it seems counterproductive to medicate someone without addressing the root cause of the anxiety. There are also several effective therapies that don't require medication. Working together, your daughter and her mental health professional will have to identify and test which therapies will be effective for her.
It's wonderful that you're involved in her healthcare and that you're seeking treatment for her anxiety. You'll find that your daughter will have to take the lead in some things, especially in finding a therapy regime that works for her. One size does NOT fit all with anxiety.
Finally, one thing that will absolutely come up is that her doctor will want to be sure that your daughter exercises. This is the single most effective universal treatment for anxiety. It doesn't fix the problem, but it alleviates the symptoms, and, if your daughter isn't physically active, it will also teach her to take time to take time, which is also important in developing self-assessment skills.