Sorry, but I think this single sentence is indicative of a serious problem. I think you have already determined in your own mind that holding your nose during your class is "getting by." If your instructor allows you, for some reason, to do so, will you be prepared to handle a lost mask on a post-cert dive by holding your nose and closing your eyes? It would be foolish to put yourself in such a position, but it would be your choice. But you would not be preared, IMHO, to buddy with anyone. You owe them more readiness than you are apparently willing to provide.
I believe you can overcome this problem with slow, gradual exposure. I think you need to talk to your instructor about giving you credit for the pool work you can complete successfully, and delay the rest of it until you're ready. Don't cheat yourself out of the thrill of a great sport!
Having said that, I'll say up front that I'm not an instructor, and your instructor may totally disagree with my personal opinion.
So just checking here - you think that you should be able to open your eyes and not hold your nose before becoming a responsible diver? From what I gather a lot of people keep their eyes closed underwater so wouldn't it be the same for them losing a mask? They are unable to see to recover it and my holding my nose wouldn't make much difference in that scenario. That's where my buddy comes in - right? You say I owe my buddy more readiness than I am apparently willing to provide. That is incorrect I am willing to learn what I do not know and that is why I posted.