This word consists of kanji with hiragana attached. Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means swelling so the verb vocab version is to swell or to become inflamed.

腫れる is used when a part of the body visibly swells up, like a swollen face, a bug bite, or puffy eyes from crying.

The reading is the same as the one you learned with the kanji, and that sure is… swell.