I could not tell from your note if your son will be in your class, and I do hope the answer is no. If your son is in your class, I think it will be impossible for him to fall asleep without nursing, unless you begin now helping him to do that with you at home. So if he is in your class (which would be hard for him for many reasons -- it's like suddenly having to share you with a whole classroom of siblings!), you will need to begin immediately NOT nursing him to sleep at nap time.
You do that by first acting out a scenario with stuffed animals in which this happens, so he understands what you mean. And then you just explain that he can't nurse to sleep anymore but you will cuddle him, and then you hold him with every bit of compassion you can summon up, and acknowledge his deep grief about it. He will wail and rage, but every day it will get better, and at some point, he will roll over and go to sleep. Be prepared, of course, for more nursing at other times of the day, since he will probably panic about the availability of your breasts. And make connecting with him in other loving ways your top priority.
The great news is that your son is able to fall asleep quickly and easily without nursing when your husband is with him instead of you. So presuming he is not in your class, he will be able to do this as well. Of course, that won't work if you ever nurse him at school, so he needs to know that at the school, the nursies don't work. And the truth is that if you can get him falling asleep at naptime without nursing, it will definitely make this adjustment easier, because he won't even think to ask.
I would also say that nursing every 10 or 20 minutes does sound like he is nursing for emotional reasons. Maybe he is in pain -- teething? But almost certainly, nursing that often is about emotions. Boredom, possibly. But more likely, he is using nursing as a way to keep his upsets down. That might be why he cries for hours when he doesn't get to nurse. He can't use the nursing to stuff down the emotions, and the feelings swamp him. So if he is crying a lot, I would remember that he really needs to get those tears and fears out of his system, and really encourage him to cry.
Congratulations on your job, and good luck!