Most tattoo artists and piercers will not work on you if you are breastfeeding. The main reason is the chance of infection and it being passed to your child. Your ideal bet would be to wait until you are completed breastfeeding. It's not worth the chances.

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i wouldnt risk your childs health for a tatto or piercing…..just be paitient and wait it out….

(also i wouldnt wear any peircings near a baby…they tend to grab at everything…..i dont even wear stud earings cuase ive had a baby grap them and pull)

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I concur with Mika. Most artist won't work on you while you’re breastfeeding. My hubby won't.
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I wouldn't chance it. Just wait the some odd 3-4 months. then get the tatoo or piercing. Patience.
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Why would you want to at this critical time?
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No!