Oops. I've had a chance to hit the books, Bambi, and I see that on the third part we're both right-- and both wrong. Pungo is indeed pupugi or pepugi, as I thought, but COMpungo is compunxi, as you wrote. One of the things I like about this forum is that I learn something here every day.
I see also that Cicero seems at least once to use compunctum (or conpunctum, in the Loeb) to mean "tattooed" (De Officiis ii: 25). The problem with this is that a few lines further on the text suggests that the tattoo in question may have been a stigma, or nota-- that is, a sign of infamy tattooed or heat-branded on a criminal, or on a runaway slave.
Cicero does speak in that text of a "tattooed barbarian" (or perhaps a "branded barbarian"). Could this be the text you were thinking of, SP?
If we are willing to accept compungo as "I tattoo" in a general, and not solely in a punitive sense, I suppose we could for the substantive use the infinitive in the nominative, and the gerund in the obliques.
So "I have a new tattoo!" might be Habeo compungendum novum, literally, "I have a new pricking". I'm not crazy about it, but it's probably better than my imported word.
Gratias tibi ago, Bambi.