I live in a country where personal privacy isn't all that respected. Recently, I've encountered a problem. It seems that some people are aware of some info that I posted in some sites on the internet.
If only one of those sites was in your country, that would explain it. The website will have the IP address of posters and the ISP knows whose account was using it. OK, that doesn't prove who was actually using the computer, but:

and no one else uses my computer.

If you happen to have cable or satellite then you probably have a static IP address which makes the trace even simpler.

I got spanked by my company for once posting on an internet forum from my company computer and it was done anonymously.
Most companies monitor (log) internet connections from their servers. They would see the traffic going out as well. Most websites show the date and time of posts. You don't need to be a FED to figure it out from there.