Hi there. I can relate to your post, so I thought I'd offer up my thoughts.
I think dating in the workplace can be tricky, first because if you're not careful you could easily get fired and second because you may be forced to interact with a person who rejected you. That said, if you're careful with your communication and you think you can manage working with someone who romantically rejected you, then it may work. Office relationships definitely do happen. I've dated two coworkers in my time, though neither of the relationships really lasted that long.
Before going further, I want to suggest that you move on from this lady. According to your writeup, she directly told you that she has a boyfriend and that she doesn't want to go to the park with you alone. That's a rejection, and it sucks, but it is what it is. It happens to all of us, and it's totally cool. You took action, and that's what really matters.
As for "spilling your feelings" I would not advise that. This lady has already made it clear she's not interested, and if you roll up to her and unload some hefty feelings on her it will probably make her very uncomfortable. Maybe you could say something like, "Totally cool that you have a boyfriend. If anything changes please keep me in mind." That shows her respect and keeps the door open at the same time, no hefty feelings needed. Other than that, I would keep the relationship professional and continue on as a friendly coworker.
When you say you asked for her number and tried to get her on a date, was it crystal clear to her that you intended it to be a date? If you simply asked for her number and then texted her about checking out a park, it may have been ambiguous to her. For future reference, I've always found it best to just be direct about what you want. For example, "I'd really like to get to know you better. If you're interested, let's set something up" or "I'd like to go on a date with you, would you like to set something up?" Anything that clearly states your intentions/desires is better than ambiguity in my opinion.
As for the obsession part, just focus on doing fun things and meeting other women. Go check out some museums, explore your town, go to concerts, and do other things you find interesting. You'd be surprised by how things can change when you go out and live life.
Hope this helps.