Yeah I have gone through the same thing in school, I have stuttered a lot while giving the annswer which I already knew, I have felt really bad afterwards, the memories still haunt me but the thing is nobody else remembers it now , the teachers, your friends, nobody gives a s*it down the line.  I developed a mechanism for these times, I used to fake clearing my throat / cough multiple times (5-6 seconds) and go through what I have to say in my head and remind myself to keep calm and tried my best. I still stuttered though , but it was much better than before.