You must be that isolated regional holdover. 
I also have American parents, deep Mid-West American roots, was raised in the Mid-Atlantic and have ancestors with the same UK locations as yours, and I never heard whinge till I found this message board. I’ve still never heard it actually pronounced outloud.
My alternate theory is that we were just a really annoying collection of kids, which necessitated frequent employment of the word, and you and others were exemplary angels, so you never heard it. I note that I associate the word with children and it has a connotation of childish behavior. I’m not sure if I feel the same about “whine,” in spite of the higher pitch it has in my mind. “Whinge” is somewhere between a whine and a grouse, which is slightly above a grumble.
My mother would beg to differ. I always heard, “I can’t understand you when you whine.”
One day I heard it pop out of my own mouth, said to my then 2-year-old cranky daughter. I knew I was a grown-up at that point. :eek:
Aspirating.
Whinge is to “Winge” as What is to Watt. But, interestingly, Where’s equivalent is Wear, not Were.
Whine and Whinge are not the same things. Whining is high pitched and elongated. Whinging is more like grumbling.
“A ship is a thing that on water floats;
The large ones are vessels, the small ones are boats.
Which ones are vessels and which ones are boats?
–Pardon me while I look at my notes.”
By another system of taxonomy, a ship has three or more masts, all square-rigged.
“Stop your whinging” was a popular reply from my grandmother (irish) when a child was complaining about not getting their way or something they wanted.
I hear it on a weekly basis when in Ireland.