I really want to know if Byul is an alpha or an omega ! （/TДT)/ did I miss it?

Nope. You didn't.
They don't get identified until around 4th grade or something? Also this is pretty much just an initial test and they do get tested again in middle school. (If i didn't remember wrong?..)

I remembered them assuming that Byul is a dominant alpha since like Dojin, Byul reacted to the pheromones of his parents while they were fighting or something.