@Pat ********
you will be able to apply for tourist extension all the way up until 20 days of overstay. They'll just fine you, stamp your passport, and then give you a retroactive extension. That means if you go 3 days overstay you'll only get 27 days from your extension because they will date it back 3 days, and you'll pay 1500 baht overstay (500 per day).
But you need to be aware that you'll also be fined for not cancelling your education extension. You'll need a letter from your school that states the last day of study, and you'll be fined 500 baht per day from that day (up to 20,000 baht)