Do you think it's a bad idea to fall for my coworker?
What makes you think you're falling for your coworker?
I was feeling just as I felt for my girlfriend, if this happens this thing could be real love.
It's common to become attracted to someone that you work with. I think if your coworker feels the same way about you then you should ask them out.
I want to but she has a boyfriend and I don't want to embarrass myself.
Considering you both are already in relationships I recommend staying away from this. If you continue to try to pursue this is only going to end up bad for you.