By beeping sound, does it come and go like a song beat or rhythm, like beep beep beep beep, or is one long ringing sound, like beeeeeeeeeeeeep? You may be suffering from some Tinnitus, but I hope not.
As far as tube sound goes, the flavor of it seems to vary pretty greatly depending on which tube you use from my experience, like about as much as using a different brand of headphone, but a good unit can certainly be very detailed. I actually think the decay between notes/detail nuances is shorter in my tube amp with the Sylvania tube than with my FiiO E12 solid state amp, which helps make the detail more distinct (I usually start calling it the "texture" of a note at this point, very addictive from the time you first hear it). There are "good" and "great" tube amps, just as there are "good" and "great" solid state amps. One thing I will say though is it's easier to get solid bass and treble extension with a solid state amp, but really I just enjoy the tube amp a lot more.
I've only tried three tubes so far, but I agree that (so far) the highs feel less extreme/harsh against my head with the tube amp than the solid state. I have 5 tubes that have been sitting in a box, waiting for me to try them, for 8 months.