I can definitely relate. I'm also a Christian with GAD and my anxiety has really impacted my faith over the years. I go through periods where I get trapped in a profoundly negative view of the world and think that perhaps faith is just something we use to cope with how awful reality is. This tends to lead to an intense downward spiral of fear, depression and despair. I even have a theology degree, but that doesn't help much when I start to have doubts and get stuck in a rut.
It's helped me to recognize that those doubts/existential fears are spawned by anxiety, not reason or logic or evidence. I've also realized that anxiety gives me a profound intolerance of uncertainty (or things I perceive as uncertain). Striving for certainty is a futile quest that will lead nowhere. The only thing we can be certain of is that uncertainty is a core part of the human experience. Learning to accept uncertainty -- and freeing myself to simply do my best based on what I think I know and believe -- has given me some relief from the paralyzing fear of the unknown.
I've also found that it helps immensely to spend 10-15 minutes every day praying, reflecting on my faith and grounding myself, focusing on hope and beauty rather than negativity. The things we choose to think about and focus on can shape the course of our lives. It can help immensely to simply let go of the troubling uncertainties and existential questions we have. Sometimes I imagine those thoughts/fears/obsessions turning into bubbles and simply floating up and away, beyond my reach. If I'm feeling really down, I'll also watch Lord of the Rings -- for me, that movie (and the books) seems to perfectly capture the fundamental hope and beauty in life despite its horrors.
One other book that's helped me is Greg Boyd's "Benefit of the Doubt." It's a personal and theological reflection on how we can accept doubts and use them to deepen our faith, not shatter it. I highly recommend it.