Define "background fuzz sound." Can you post an example?
Are you talking about hiss? This is usually self-noise from low budget mics, mixers and recorders or the camera if you are recording audio directly to camera. If not, it is can be a noise in the ambient environment or some sort of interference. Were you monitoring with headphones? If yes, which headphones? Did you hear it when you were on the set?
And BTW, there is no such thing as a boom mic. Mics are mounted on a boom-pole, such as a shotgun mic. I'm sorry to be picky about this, but you should learn correct terminology. You could say boomed mic or refer to the specific mic which was mounted on the boom-pole.
And next time please include all of the pertinent details like the make and model of each piece of gear in the audio chain, the settings that you used, what was recorded and where (dialog in a kitchen, for example), etc. It's like saying "my picture is out too dark; what do I do?" It's hard enough to troubleshoot and even harder by remote control without specific details.