I know that I can see the data usage of my iPhone 4(iOS 6.0.1) under: Settings → General → Usage → Cellular, Usage , but the counter has a bug - now it's showing over 16GB(for 2-3 hours tethering). Any Idea of the reason for this bug? If I use some app for counting the data usage, would it show the right usage?
That is probably just a bug in the data counting mechanism. You could download your carrier's app to test how much data you have really used.
Another thing to try would be updating your iPhone to 6.1.3. There are always some bugs fixed in each release, and maybe this is one of them.