If you have WinNT you can just run perfmon and add the dial-up connection to the monitor. This won't break it down by app, but will help.
Also, not on the subject of breakdowns by app, it sounds to me as if you're getting pretty normal performance. "A few internet browsers" and "a few downloads" concurrently, with the downloads running at 2Kbps is probably all you're going to get.
I know it doesn't seem right, but 56K modems never run at 56K (first chunk of bad news). The best you can ever get is something like 52 or 53Kbps. This is under highly idealised conditions. Normally expect >46Kbps.
Then consider the way modems talk (asynch and all that), and you're lucky to have half of that available for actual file transfer. Then on top of that (what, there's more?) is the effect various encapsulations have on file transfers, which is to chop the source file up, encapsulate it, send it to you, de-encapsulate it and put it on your disk. All of this requires processing which meansthe downloads have to wait, maybe even re-try from time to time.
Oh, and you're pulling those files across the Internet (I assume). Which means that there are at least a couple of network links of "unknown properties" between you and your files. The bottleneck can easily be "out there" (which is why even broadband users do not necessarily have wonderful performance).
What to do about that? Well, besides "broadband", you can try closing all but one browser, and all but one file transfer. Also, close down all unnecessary processing on your computer (look for other applications and systems services in the SYSTRAY). You should see that 2K crawl up to 3, or maybe even 4.
I know, that's not what you asked, but hopefully it is information for you that helps you understand why you will never achieve 56K downloads.