>I didn't think about it before my Ceremony of Twelve.

This is a very simple statement; whatever *it* is, you did not think of it before the Ceremony of Twelve. It says absolutely nothing about whether or not you thought of it *after* the ceremony; you might have and you might not have, but no implication is made either way (without further context, at any rate).

>I didn't think about it until after my Ceremony of Twelve.

This means that you *did* think about it at some point, but not until some unspecified time *after* the ceremony. I don't agree with Daniel that you could have thought of it *during* the ceremony; it quite clearly states that you did not think about it until (some point in time) *after* the ceremony. But you did think of it. 

So the sentence using *until after* is much more likely. The version with *before* is a perfectly valid statement, but it doesn't seem very useful. "I didn't think of it before the ceremony." "Okay, but when did you think of it? Or did you at all?" It just doesn't give much information.