Is there a program available that will show me how much certain files are GROWING over time?

You could monitor it using DiskPie, I’ve had it for a few years now and use it pretty constantly. I’m one of those people with a terabyte of storage and 1mb of free space. I shuffle things and prioritize constantly. If you run it once a week on her files, you’ll see a breakdown of folders, percentages of space, exact sizes, etc – keep a log and you’ll have the info you want.

Based on your last sentence, DiskPie is exactly what you need. And it’ll show you some surprising things that are taking up space you may have forgotten about.