Grammatically, it looks fine except that I would omit "the" in "the third period" (it is common to use the "zero article" before school periods, just like we say, "in seventh grade", etc.). If you mean to say that you stayed for third period and only after after it was over, I would change that to: "After attending classes through third period, ..." I would say "until third period" technically normally means "until third period started".