A few minutes later: The experts say that the Software Update option in Settings, About Phone, is not removed by rooting, although of course, the ability to update the software is removed.
You shouldn't be rooted. Root is something that can't be accidentally turned on. Most of the time it is a series of several steps, involving locating, downloading and applying files to attain root access.
What phone do you have? I remember reading that in some specific models you can check the system updates if you tap on 'android version' or 'system version' in settings - about phone.
Just run Root Checker. It attempts to gain root - then it tells you whether it did or not. If it did, the phone is rooted, if it didn't, the phone isn't rooted. (An app that looks to see what files are available may or may not give you the correct answer - one that asks for root always gives you the correct answer. If running Root Checker doesn't pop up a window asking whether it should be given root access, the odds are that it will report that the phone isn't rooted.)