Talk

anyone...x

Are you sure you can't get time for an interview? What would happen if you had a medical appointment for example? There must be some situations where you would be able to get away during the working day?

Apply for some jobs (believe me it will make you feel less trapped), and if you get a good interview say you have the dentist or your car won't start or make some other excuse. Try and get the interview right at the beginning or end of the day or at lunchtime. When they ask for references tell them not to approach your current employer yet as they don't know you're looking. Don't feel anxious, obviously this is quite a common situation.

When you say the job is nothing like what you expected, I assume you are not actually in a teaching role at the school? How much notice would you have to give before leaving, as many education jobs require a term or half-term? Is the role one where you would resign and do temp/agency work - without knowing what you do at the school, it's difficult to advise further.

Most prospective new employers don't ask for a references until an offer of employment has been made as they know you don't want your current place to know you're looking .
I've just got a new job start in a couple of weeks and my offer is subjective to references.