A girl who is engaged likes me and I like her, but I'm getting mixed signals, any suggestions?

It is about a girl I work with and I have developed a fast friendship. I've gone out of my way to be totally respectful of her current engagement. It started out as just casual conversation and a few rides home from work. I knew she and her fiance were going through a tough spell from what she'd shared and from what she'd been eating at work, so I bought them some groceries on one particular ride home. We have a lot in common, very similar backgrounds, taste in music and culture. We've also both lost parents at a young age. At one point, around my birthday, I became noticeably depressed. She came to my aid quickly. I talked with her and she started telling me solid Christian answers to my dilemma. We that night e-mailed each other and had really good conversations about music, her, me, our plans for life. I was then starting to like her. The next day at work I asked if I could get a moment alone with her. I told her that I wanted to limit our contact as I've started to develop feelings for her that are, to me, inappropriate as she is engaged. She told me that maybe we were just meant to be friends and there is no reason to limit our friendship. She then told me a story involving one of her friends(who had a crush on her fiance), herself and her fiance - how they(she and her fiance) kept their relationship a secret from their friend so they could develop a strong Christian bond and eventually show the friend that the crush was just a source of bringing her closer to Christian friends and God. I was offended. I felt tricked. I felt as though she was trying to evangelize to me. I didn't talk to her for a week or so. We ignored each other at work. She then sent me an e-mail explaining herself. She really cared for me she said. She was sorry and misspoke. I apologized for being brash and we "made up". The very next day at work she came to my door and knocked, with a huge smile on her face during the whole conversation, and said she has something to tell me, but can't at work so she gave me a note with her # attached. She said to call after a time that her fiance leaves for work. I didn't call that night and got an e-mail from her wondering why I had not called. I called that next night and she said she wants to meet me in person. We met at a mutual location and had a few drinks as she was very anxious and had been having panic attacks all week. She told me she has fallen for me, not in love, but feels very sexually attracted to me in a way she has never felt before. I told her that I cannot deny that I do, too, but she is engaged and I will not allow anything to happen. I told her my feelings for her are very strong. She asked me how we can make her feelings go away. She wants to stay engaged, not cheat, extinguish the feelings, and continue our friendship. I don't see how that's possible. I have never felt like this so quickly about a woman. She tells me she has never had feeling like this for a man. The way it ended last night was on a very sour note. Help!?!