I see that you have decided to keep the program - which I think was a good decision, especially the way you describe your situation, with a very small support network where you live.
When I first read your post, though, I had some immediate thoughts about your question... When you buy groceries, I would guess that you don't really know a lot about the store owner's religious convictions, or for that matter the board members of Kraft's or Proctor & Gamble's religious views...?
You probably still buy their products and eat the food, and they make you and your family full and keep your house and laundry clean. I do understand where you are coming from, though, because I believe in consumer power and that by carefully choosing what we buy we can influence the ethics of businesses - I buy organic and fair trade products because pollution and economic inequality/poverty concerns me. But it's hard to get everything you need according to such strict guidelines.
Also wanted to share that when I first read about the program, I was actually a little turned off by the reference to prayer, because I am not involved in organized religion and thought, "Oh, here we go - the Lord is going to save you. Well, what are we supposed to do who can't go with that solution?" I still got the program, because it's based on science and hard work, and that I can relate to.
I'm not sure how to phrase my last thought without offending you... but please understand that I am genuine when I ask - how come that you can not share your problem and have to keep it secret? It is my understanding that a Christian fellowship is supposed to be loving, understanding and supportive... If I was a member of a religious group, I would expect them to be the first people I could go to if I was facing hardship and challenges?
I ask because I know from experience that keeping anxiety and panic a secret makes it worse. It adds to the problem. If you tell the person you are with that you are feeling bad and it is because you are having an anxiety attack, a lot of the anxiety will dissolve simply because you get rid of the part that is about fearing the reaction or losing control in front of someone who doesn't know, or even the fear of scaring them. Having someone at work who knows, will help you feel much better immediately - it's like a lifeline. I would hope there is someone you could consider talking to, I am convinced that it would really help you feel better immediately.
Take care,
Arwen