White noise machines are expensive, and have never worked for me. Even with my fan on sometimes, I can hear little noises, like one of my cats sneezing. If I'm having a tough time trying to get to sleep, I move as close to the fan as possible so that it's literally the only thing I can hear. I've probably looked like an idiot over the years when it's time to buy a new fan. I make sure I find an outlet to plug one in, so that I can hear how it sounds.
Box fans are by far the best ones to buy.
You might try it. It certainly can't hurt.