Looks like the school administration is quite right. Assuming that you are a citizen from one of the countries who will get a 30 days visa by arrival you will have to leave the kingdom and re-enter to get this 30 days visa - whether it's not in your plans or not. If you want to stay even longer you may need to apply for an extended visa at an embassy or consulate in e.g Malaysia, Myanmar, or Cambodia.

Since you supposedly are in Thailand right now I would advice you to visit the local Immigration Office to get further information.