Whiny is an adjective meaning habitually complaining or of or like a whine.
Whiney is the same as whiny, but it appears about a fourth as often (whiny is preferred in all main varieties of English).
Whinny is the sound horses make. It’s synonymous with neigh.
Whinney is (1) a surname, (2) an unusual spelling of the female first name usually spelled Winnie, and (3) part of a few place names (e.g., Whinney Hill, Whinney Banks).
Rather than dismiss Gen Y as entitled or whiny about the economy, campus career service experts need to consider the effectiveness of our approach. [Washington Post]
By the end, Gingrich came off not as resolute but whiney and mean-spirited. [Guardian]
They knew I was coming and had brought him into his stall for me to see him. I called to him from the door as I entered the barn and he answered me with a whinny. [Orangeville Citizen]