E.J.
I don't see why you couldn't get a tattoo or a piercing with a thyroid condition. My son has hypothyroidism and so does my mom. She is not tatted or pierced, but I guess she does have her ears pierced and as far as I know she's never had a problem w/them. My son does not have any tats or piercings (he's only 6!) but he does have a feeding tube surgically placed in his tummy, so in a sense his stomach is pierced! :-)
Thyroid conditions are surprisingly common. My son is on the same med as you only he only takes 25 mcg. My parent's dog also has hypothyroidism!! haha The good news is that a person can live w/out a thyroid at all (in the case of thyroid cancer)!!! So as long as you keep up on your meds I think you are safe!!
Good luck! :-)