My current CRT seems to make a sort of noise like that, it's worse at different refresh rates/sync freqs. Right now I have it at 1024x768 @ 75Hz, and it's not too bad. But sometimes it starts getting worse, so I bang on the side or the back of the CRT and that sometimes sort of fixes it. Sometimes it makes it worse. It's a minor whistle, not a shreek, so don't think that it's going to blow up. That usually happens more often when the monitor makes a "zap" sound, and then starts doing it often or repeatedly. I've lost two monitors right after that started happening, although one of them would occasionally "zap" since the day that I bought it new.
Even besides that, I can hear any and all CRT's high-pitched sync freqs though, it's really darn annoying. I guess I can imagine what dogs must feel like when you blow a dog whistle. Guess I've always had somewhat sensitive hearing.