'inflamed-eyed' is a modern compound formed from the past participle 'inflamed' (from the verb 'inflame') plus the adjective-forming element '-eyed' (from 'eye'), meaning 'having inflamed eyes'.

'inflamed' comes from Latin 'inflammare' ('in-' + 'flammare' meaning 'to set on fire'), passed into Middle English via Old French and Late Latin as 'inflam(en)'/'inflame'; 'eye' comes from Old English 'eage' (from Proto-Germanic '*augon'). The compound 'inflamed-eyed' is a descriptive formation in modern English combining these elements.

Originally 'inflame' literally meant 'set on fire' in Latin; over time it developed the medical/figurative sense 'cause redness, heat, or irritation' and now in 'inflamed-eyed' denotes eyes made red, swollen, or irritated rather than literally on fire.