A: You shouldn't be worrying about the done thing; you should be worrying whether your next decision is going to be any better than your last one.
You only 'think' you've made a huge mistake. It's obviously early days. New office, different daily journey, strange colleagues, no in-jokes, nothing comfortingly familiar: you need to allow all these temporary experiences to settle down before you do anything precipitate. I don't suppose you much enjoyed your first term at that new school, either.
Then think a bit about your old job: what makes you believe it might still be open? I assume it was your choice to leave - so your departure will have caused at least some small inconvenience. Unless you had a very special talent (and if you had, they'd surely have worked much harder to keep you), it's difficult to see why they should welcome you back. And they'll almost certainly have found a replacement for you by now; either that or they've discovered that they don't need to.
So give this new job a good bit longer. Meanwhile, have a drink with one or two of your ex-colleagues and catch up on the gossip. You don't need to let on that you're doubtful about your decision to leave - never a good idea so soon afterwards - but you'll certainly pick up some useful information about who, if anyone, is doing your old job and how well that person seems to be doing it.
Only when you're absolutely certain that you'll never be happy where you are should you seriously consider a return. It's entirely possible that you'd be welcomed; managements can be flattered when good people want to come back, and they see it as a valuable reminder to other members of staff that the grass isn't always greener. However, do bear in mind that, if you are welcomed back, you'll lose your freedom to resign again for quite a long time. Such erratic behaviour would look decidedly odd on your CV.