Archaic medical term for swelling; in modern Japanese, 腫れ (はれ) or 浮腫 (ふしゅ) are more common.
The word 腫気 can be found in old medical texts.
The exact derivation is uncertain; the kanji 腫 (swelling) and 気 (spirit/energy) suggest a traditional concept of swelling related to bodily energy.