i'm not sure about either but i'll take a guess.

1. I've been having a similar problem with my compoiund bow, but it's not on my wrist. It's on my hand behind the thumb. I held my bow in hand and cycled the bow slowly to find out what was making contact. (for me it is my arrow rest due to my draw length being too long) try that out. Could it be the arrow's fletching slapping your wrist?

2. possibly a spine problem? The stiffness of an arrow is much more important with a trad- bow than it is with a compound. and I know that an incorrect spine rating can make arrows go side-to-side.

As I said. I'm still a rookie, just some suggestions to try