Ideally you should wait until your nipples are fully healed before doing any type of nipple play. It is important to wait through the entirety of the healing process because until 9-12 months your body has not finished developing fistulas. This means that you have a higher risk for ripping or tearing the piercing.
Subsequently, do nipple piercings go through the nipple?
From the piercings I’ve seen, it is generally done like that- not directly straight through the nipple, but around behind it, mostly through the areola. Considering the fact that most people don’t have enough actual nipple to safely hold a piercing in place, I’m surprised that this would be expected.