This is from a Manga, or so I heard.
Maki-chan squeezed around a/some local school in the era/period during junior high school.
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This シメる is a slangy verb that euphemistically means something like "to chastise (thus making them understand who is the strongest)" or "to give someone a (harsh) lesson (about underground rules, etc)". Usually brute force is implied. It's 締める in kanji, but normally written with katakana. This ～て回る is just "go to various places (doing ～)". So this girl went to many schools in the area, challenged school delinquents, defeated them and dominated them.