Please help with coworker crush!

So I've never posted here before but I am kind of at a loss with this situation.
A little background: I'm a guy, 32. Soon to be a lawyer. She is 30, soon to be the same. We started at a new job on the same day about 2 months ago. I was attracted to her immediately but was honestly a little intimidated by her and by the new job environment to really flirt or be myself around her at first. That changed pretty quickly. We ended up spending a good deal of time together alone and there was definitely chemistry. I noticed her looking at me in "that way". You know what I mean. Holding eye contact for extended moments and she would have this enormous smile on her face when we'd see each other in the morning. I becoming more and more drawn to her really fast.

The situation arose over the past few weeks. Our team went on a happy hour outing after work and we were joined at the hip the whole time. So much so that I didn't want people to start whispering about us. Office gossip can be a problem. So she was taking a week off the following week to take the bar exam. That Friday I bought her a book and a nice card and left it at her desk. She seemed to really like that. We went out for lunch alone that day and I swear the chemistry was ridiculous. I told her at the end of lunch that she should get her answer ready,because when she came back to work after the exam I was going to ask her out. I got that enormous smile again.

So the week passed and she came back this week. I let Monday pass and emailed her Tuesday to go out to lunch again. She texted me back instead of emailing, giving me her number. Clear signal right? So at lunch I gather up the courage to ask her and I do. I say "you should let me take you out to dinner". Huge smile. "I should huh?" "Yes I think you should ". Then this: "well, I'm kind of in a 'it's complicated' situation right now so..." I was speechless. I had specifically asked when Valentine's Day was coming up and her birthday what she had planned. She knew I was asking if she had a boyfriend. And her answer to both was having dinner with her sister.

So I don't know what to say. I really didn't see that coming and am at a loss for words. I try to wrap up our lunch and get away from her because I feel totally awkward and embarrassed and honestly have no idea what to say now. I manage to ask her if I was just totally in left field with asking her, to which she says no that was probably her fault.

So here's the problem. I know this girl likes me. And I really like her. I know she purposely never mentioned a significant other in front of me because she could tell I liked her and didn't want me to know. I'm no stud and I'm not arrogant, but I know when a girl is interested and when she's not. And this one is. At least enough that she entertained the idea of going out with me. The issue is what I do now. Everyone is telling me to basically ignore her at work. No more lunch dates or getting coffee. Just pretend she's not there more or less. Which is totally not what comes naturally to me, playing it cool like that. I want to let her get to know me more, let me make her laugh some more, and hopefully she'll decide she wants to go out with me. I know from experience that this a super delicate moment and if I have any shot with her at all I could ruin it really fast by handling this the wrong way. I got lucky in a way that next day after this I got a terrible flu and went home early and missed work Thursday and today. I honestly think I was so crushed by her response I was worn down and ended up getting sick. I really was totally crushed that afternoon. I barely remembered what that feeling was until now. I haven't felt it years. Rejection is fine, but this was different for some reason.