You may or may not have a degree. You may or may not already be sitting the tests to obtain a teacher's license. All your concerns can end but begin again here.
The good news is that because the Teacher's Council of Thailand (TCT) is trying to rigorously enforce the need for all foreign English teachers to sit the tests for a teacher's license, many schools are now finding it difficult to retain staff. This is becoming very visible in Isaan, for instance, where many schools recently made a complaint to the Ministry of Education which, in turn, lodged a complaint with the TCT.
But I digress. Headmasters are now being wooed by recruitment agents, many of whom have fledgling private language centres, and can recruit whoever they please (criminal record permitting, but only in extreme circumstances such as when a foreigner/teacher has been accused of a crime and schools have to demand to see staff backgrounds).
Contracts are made between the agent and the employee (the school stays well out of this equation). The agent arranges the work permit and because the application is being made through a private language centre, there is no need to have any advanced academic qualifications, no need for TCT waiver letters and no need to bother with teacher's licensing tests. The school merely submits salary applications to the authorities and then splits the difference with the agent.
Which brings me on to the bad news. Teachers are only paid by the class and receive no money for sick days or holidays. Likewise, they receive no other benefits, such as limited accident & emergency. And teachers are running just as much risk as schools and agents. Surely this unethical practice must be breaking certain laws somewhere along the line. Top tip. Make sure your agent is well connected and greases all of the appropriate palms so that the authorities turn a blind eye!