I wish I had your advice when I was trying to deal with the pain of an open-office work environment. Listening to music or white noise for 8+ hours per day to drown out extremely noisy coworkers has left me with very nasty tinnitus. I am hearing it as I type this, more aware of it than I usually am, and I wish I was back to a state where I could just hear the world without the constant accompaniment of a high-pitched 'eeeeeeeeeeee'.
I have read in some places that everyone hears that "eeee" to some degree or another. I distinctly remember being able to perceive that sound even when I was a child, and I have read anecdotal reports from many others. (I did some research on this when I was going through some kind of pseudo-hypochondriac attack.) I don't know how true this is, but it might offer you some comfort.
Like pain becoming more acute when you think about it, this sound always seems louder to me when I'm stressing about the health of my hearing. I notice retrospectively that I never notice it when engaged in any other activity, even if it's very quiet about.
My symptoms are a little different, I feel: it is pretty quiet now and I am about as relaxed as I get but it is pulsing away as I type this. It is good to hear (ha) that it might be more common than I realize - everyone else I have talked to about ringing mentions a different experience than mine so it is good to hear that my case is not too out of the ordinary.