You could just say: "my fourth period." Every native would know that you mean 'class', and that's what we typically say: just "Fourth period." As for the rest of this, it depends on the context, but if you're saying this to someone RIGHT NOW, then it's very good. If you're saying this after you went home, then it should be "could go home earlier than usual" Does that make sense? Hope this is helpful, great job.