First, be on the phone with a source. Make that a very helpful, important source. Scatter a few coughs throughout the interview. Then, when he's telling you something very important, start coughing more... uncontrollably, in fact. That's good. Now try to tell him you're sorry and you've been very sick, but choke on the words instead. If you're doing this right a degree of panic will now be in his voice. He should offer to to call an ambulance for you. In a brief respite tell him you're... cough, cough... fine... cough, cough, cough. Then rasp, as creepily as possible, "Thank you for all your help."
Once you're off the phone, start coughing like you really mean it, to the point where you're gagging and very nearly throwing up. Make sure a single tear falls out of your left eye and dramatically down your cheek for effect. This fit should last a good five minutes, despite the water you're gulping and the cough drop you're furiously sucking on as if it were the sweet teat of life.
You should have brief spells of repose in between your coughs so your coworkers think they can finally get some work done now that The New Girl has finally shut up before you start up all over again. Get so worked up you're all sweaty and your face is the same color as your red sweater. If you're really enterprising, sprinkle some trumpeting nose blows in there. Good. Real good.