Everyone's worst nightmare! Heading through airport security can be a nerve-wracking experience, even if you don't have a metal object embedded in your skin. What if my piercings set off the alarm? Now everyone around me is going to know my nipples are pierced!
First of all... Be proud of your nipple piercings!
Second, let us ease your fears about metal detectors... Although there are certainly some exceptions (like an overly-sensitive detector, lots of piercings, or large-size jewelry), most body jewelry is going to pass through a detector without much hassle. Metal detectors are designed to detect actual threats like guns, knives, or explosives (and not false alarms like the wire in your bra or a pen in your pocket). Because most body jewelry is small and harmless, you'll probably walk through the detector unscathed.
Here's the catch - new piercings really should not be removed for any reason. Because of this, especially if your piercing(s) are fresh, your best bet is to just hope for the best. If you are put into a position where removing your jewelry is the only way to move on, give your local, professional piercer a call when it's time to put it back in.
Finally, if you're passing through an American airport and your jewelry does happen to trigger security, you always have the option of a quick visual inspection by a TSA agent of whichever gender you're comfortable with.