J.W.
Unfortunately, there's not much you can do but keep trying to correct it. More than likely its going to get worse. My daughter is 4 1/2 and whines almost everytime she doesn't get her way. And boy she can kick it up, especially in public. If she whines too much she goes to time out. If it continues after that, she loses her star for the day. On good days she gets stars put on a calender and when she gets so many of them she gets a prise. Some days are tough and others are easy. I do notice that it is worse when she needs a nap. Grin and bare it is about all you can do. Just don't give in. Good luck.
J.