There are definitely many different types of therapy that people go through when dealing with anxiety. I have taken Zoloft in the past with very favorable outcomes, but the most important step in dealing with it was to go seek counseling. I do not believe you can truly be 'cured' of your anxiety unless it is confronted and dealt with. Some people choose to use medications while others do not; it is definitely a personal choice in my opinion.
People will report very different outcomes, so it's impossible to say what worked for one will work for another. There are a great variety of natural remedies that are used in combination, not singly, for the treatment of anxiety. However, since your child is only 15, not only is Zoloft considered problematic by the FDA, but so can natural remedies be problematic. So rather than specific recommendations, I would advise you to consult a naturopath or a psychiatrist who practices integrative medicine about natural approaches. A good book for you to read about what's available is Natural Highs by Hyla Cass, a psychiatrist at UCLA, but again, her recommended dosages will be for adults. Good luck.
Such a young age to get such a big condition. I would be in favour of theraphy at that age. Since she is so young the root cause of the problem may be a lot easier to find and deal with. Theraphy teaches you coping skills and gives you a better understanding of your condition. When it first kicks in you are wondering what on earth is happening to you. Why you. Your body and mind go through a lot of changes. There is so much going on at once. That has to be all tackled and adjusted to a level were your daughter might understand the answers to some questions that are playing over in her mind and learn new ways of dealing with things when outside of the house. For the record I was housebound for over a decade myself. Used to be a living nightmare just even thinking of stepping outside that front door. But it had to be some day. With me it was a mixture of medication and theraphy. Medication is only about 1/3 the answer. The rest is up the sufferer. To want to take those steps out the front door. Nothing major to begin with. I stayed in my front garden to begin with. Until I felt comfortable there. Whole idea was to not run away from the feelings that I hated the most. To let them kick in. And see that they do pass. Just as they came on. It can be a slow process. But if you try take on too much too quickly you may fall a lot harder. Make the situation worse. Baby steps. She has to learn the basics of existing without fear outside of the house again. It is kind of like we forget it. Everything out there is fear and anxiety. So really it is like a baby learning the ways of the world. It will be all new to her again. Frightening at first. She will want to run from it. We all do. That is normal. But the more we practice the easier it does become. That I can and will promise her. The biggest thing for her is that she has to want to do it for herself. Not for others. But it can be done. If you jump over to the agoraphobia forum here on MedHelp you will read a lot of success stories and how people deal with going back out. The two forums are similar. Just wish her all the best from myself. We are always here should she ever want to ask questions at all.