"scolded me" means someone spoke angry/harsh words to someone and usually includes giving orders not to do it again. "scolded me when I made..." means that the scolding happened at the same time/at the moment of me making the mess. "scolded me after making..." means that the scolding occurred/happened at some time following the making of the mess. "scolded me for making..." means that she scolded me because I made a mess, but it does not tell use when the scolding happened. Albert's explanation for using the preposition "for" is correct. All of the phrases above are correct.

yes! you can also say it like this, "My mom scolded me for making a mess in the kitchen."

It would depend whether the person you are speaking to or writing to is a user of American English or not. In British English the word 'scold' is almost never used. It sounds very old-fashioned to our ears - like something from a children's book from the 1930s. I suspect that many people in Britain today have never heard the word 'scold' said, and most children probably have no idea what it means. In everyday speech we use the phrasal verb to 'tell off'. " My mum told me off for making a mess in the kitchen."