I have always believed in the fact that everything happens for a reason. So if you got anxiety, something in you is urging you to do something.
I got horrible anxiety after the birth of my first child too, and like you was totally freaked out by medications.
In fact one of my symptoms was sleeplessness, and so the GP gave me something to help me sleep.
I went home with the meds, read the side effects... and never touched them.
Personally, I didn't use "willpower" or medications to cure my anxiety (which by the way is now cured... with a few niggling bouts once or twice a year which is no more than the usual human being experiences I guess).
I used "surrender". I stopped fighting, I let go, and yoga helped me to do that a lot. A fantastic book I recommend is "The power of Now" from Ekhart Tolle who is a brilliant spiritual teacher, but doesn't preach any particular religion (it sounds a bit like Buddhism to me, but he doesn't say so).
And regarding the anxiety, a book that really changed my life was "self help for your nerves" from Claire Weekes. She believes in surrender, and makes you realize that some of the symptoms are completely normal.
I remember being in a terrible state of anxiety on night, and after reading a certain chapter, having the best sleep I had ever had.
What I wanted to say was, it is possible to get better without medications, but obviously I am talking about my personal experience.
And trust me you feel a sense of such achievement after conquering it, you're ready to take on the world!!
P.S: I too have joined a church recently as I have always felt drawn to God, even as a young child although my parents were not Christians at all, I loved the bible and I prayed every single night (why? I am not quite sure), thanking God for giving me this life.
I too find it difficult to swallow certain things that are said at church, but I feel a sense of Peace there, enjoy the singing, enjoy the praying and the sermons. So I would advise to carry on doing what you feel is right, even if you do not agree with everything.
I am sure everything will turn out for the best, take care xx