Yay! I can be useful!
I'm an audio engineer, so I can answer this one. The ringing you're hearing is called tinnitus. Often people think of tinnitus itself as a problem, but it's not, it's a symptom of some other cause. There are various causes for it and things that exacerbate it... high blood pressure, hearing damage, ear infections, etc.
Almost everyone experiences some level of tinnitus whether they know it or not, but only about 20% of the population actually hears it. When I'm sitting in my control room at work (an isolated soundproofed room w/ acoustic treatments to tame reflections/transmission of sound) with nothing running, I hear it, but most of the time I don't.
You really should only hear it in quiet environments. If you're hearing it during your normal day to day activities when there's plenty of sound around, or if it's really bothering you on a regular basis, then you should probably have it checked out. A doctor, ENT or audiologist can help you sort out the cause and possibly provide treatment, although tinnitus isn't always treatable/curable.