Question about Ink in the Body... Getting more Tattoos?

So, I've got a lot of ideas for tattoos for myself - Can't get 'em out of my head. Had 'em in there for years, now...

A little while back I saw a video of an artist dragging his mag needle over a hot dog - to illustrate where the ink is sitting under your skin. Until then, I just thought tattoos were this magical thing that just appeared on your body - but they're actually INK sitting in your skin. Like, a toxic, foreign substance just sitting in your skin... forever... Some people have bad reactions to this, too, from what I've read. I have three large tattoos and have never had any health consequences from them that I'm aware of, and I know dozens of heavily tatted people as well, but I dunno. That's the one thing that has kept me from getting more; I don't want any more foreign shit injected into my body. That and the money...

Thanks for coming to my Ted Talk.

Thoughts?

EDIT: Thanks to all the kind people taking the time to go into things and link vids - very edifying.

Thank you.