Someone give me advice before someone thinks something is wrong here!

My son is just shy of three, and I think I messed up. I was sexually abused by my father when I was a kid, so I was very aware of the fact that we should teach our kids the proper names for private parts and I also made sure to tell him that they were private and no one should touch our bodies there and we can't touch other people's bodies there. I think I might have made a mistake teaching him these things.

I never sat him down to have a discussion about this stuff, but I'd just mention these things when they came up. Like in the bathtub teaching him how to wash himself I'd call the parts by the right name. Or one time he tried to wipe me after I went to the bathroom, because I wipe him, and I grabbed his hand and said we don't touch other people's butts. He saw a photo of me breastfeeding him and asked about it. I said when a mommy has a new baby they have milk in there and that's how the baby eats.

Well apparently he finds these things absolutely hilarious, so now he seeks them out. He'll go up to someone and say "Can I touch your penis?" Or "I touch [name] butthole." After seeing the breastfeeding picture he's started saying "I drink milk from Mommy's nipples!" He says these things to and about literally everyone.

I am 100% sure nothing bad has actually happened to him. He's never gone anywhere without me or my husband. He just thinks it's funny to say things I've told him not to. He gives a mischievous laugh when he says it.

I don't know how to get him to stop. I don't want to tell him that we don't say those words, because they're just body parts. And he may need to say those words if something is wrong. Plus the more I tell him to stop the more he says it.

I'm scared the wrong person will hear and it will open a can of worms. What do I do?