What if you used neosporin on a piercing?

Well considering it clearly says that in the event of a deep wound or puncture wound you should seek medical advice (it's there way of saying not to use the product on those types of wounds) and a piercing is a puncture wound. I would suggest you don't use it. Neosporin contains neomyacin and this needs the air circulation to work effectively and a lot of people are sensitive to Neomyacin. If you are washing the piercing daily using a good unscented liquid antibacterial soap and rinsing with lots of warm running water while moving the jewellery there should be no reason to use Neosporin on your piercing.