I personally also experience what you're describing and I actually have really really good hearing.

In silent rooms, almost everyone will hear a faint one pitch sound. There is at the very least two possible reasons for this that I know of: 1. True silence is impossible, so you are hearing sound waves from a long distance away that manifests as one faint solid tone - electrical currents and mobile devices can contribute to this; 2: People are not used to silent rooms, as there are so many sounds in daily life, so the brain compensates by creating a noise that isn't actually present so the brain can stay minimally stimulated - sort of like a "normal" level tinnitus.

I have OCD and I too have had far too many hypochondriac episodes as a result of constant fixation on symptoms, ailments, and such. It's so hard sometimes to distinguish normal annoyances and common pains from abnormal ones. When you worry too much, all of the medical literature and web md and personal accounts just becomes one big blur of further confusion. It's frustrating and scary sometimes to not know and it's hard to determine when a call to a doctor is warranted or overblown.

Just my opinion, seems like the sound you're describing is within normal boundaries and you're probably just concentrating on it too much.