amp trouble!

If you have a valve amp then you should get distortion when you turn up to 10. So my guess is you have a solid state amp and the 'beeping' is a kind of hard clipping. Remember that your amp interacts with your guitar, so perhaps you have powerful humbuckers that are putting a heavy load in at 10 when a 60s style strat wouldn't?

Playing guitar isn't all about pure volume. It's about the distortion you get when playing at high volume. That's why the pros still use tiny little amps like the Pignose or the Champ. They won't fill a stadium but they distort with rasp and edge.

Does your amp have a gain dial? That should be what you are using to inject growl and dirt. The other trick is to turn your guitar down in volume to 'the bite point'. That's where the point just before the string sound disappears. At this point you may be able to turn up to 10 and the sound should be alive and bluesy, even on a  non-valve amp (I can do it on my cheapo $15 tranny amp).

Sounds to me like you might need a distortion pedal to get the sound you want. Something subtle like a Blackstar Drive has real tube overdrive or at the other extreme a Metalzone will give you ultra-noise on demand.