"Pardon" is correct and understood everywhere. Some people say "Sorry" when they haven't heard something clearly, but in my opinion this usage is less common, and it may be somewhat regional as well. Your teacher is right: you are better off sticking to "Pardon", or to be formal and a bit old-fashioned "I beg your pardon."
"I apologise/my apologies" are not used to ask someone to repeat something you haven't heard. You can use them to indicate that you are sorry for some misdeed or offence.
And lastly, you should say "Should I use ..." rather than "Shall I use ..."