Sorry to hear you are sick. What did she say when you asked her to cover her mouth when coughing and wash her hands?
For future reference, here's something that might help you avoid catching colds: absolutely do not touch your face without washing your hands first. That means no rubbing your eyes, no resting cheek on your hand, etc. It's really hard to practice this but gets easier as you do it more. It will prevent you from catching whatever's going around the office.