My wife had this exact problem and it showed up during the snorkling part of our training. There is always a little water in the mask, so when she tried to snorkle, she would also suck some water into her nose.
Walter had her do this excersize and it worked.
Take your snorkle, not your mask, to the shallow end of the pool. Bend over and breath through your snorkle. If you have problems, think of drinking through a straw. Keep practicing until you can breath through the snorkle without problems. Then work with your mask on.
Walter may have some more excersizes to use, but this works very well.
Keep on trying.