The term "corked" refers most often to cork taint, or trichloroanisole (TCA). It is a fault in the wine, not always from the cork, but more often than not, which is why it's called "corked" and not "tainted." I've never heard of it happening with whiskey, but since some whiskey bottles are enclosed with a cork, I guess I don't see why it wouldn't be possible. It gives off the odor of a wet dog or wet cardboard, and even in wine it is very, very rare, occurring in less than 3% of all cork-enclosed bottles.
Anyway, like KJT said, what happened to you is not that your whiskey got corked because the cork fell in it. If the whiskey was corked, it would taste corked whether the cork itself fell into the liquid or not. You just had a shitty cork that fell into the bottle. I don't know of any other phrase that applies to that phenomenon.