Yes it was the grease -- probably. When you put it down the sink, when it goes into your pipes, it cools and clings to the pipe. If your pipes are already a little lined with gross stuff, it makes it much worse. You shouldn't ever pour grease down a sink. In fact, I have a good friend who is a plumber and he says I should get rid of my garbage disposal. They cause nothing but trouble. You are probably going to have to have your pipes rodded out -- maybe even starting in the clean-out in your basement. I doubt you can fix this one by yourself.
And yes, it's happened to me. Learned the hard way. Sorry you are too. :-(