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It looks like your eye is inflamed.
Literal
Eye [subject-が] inflammation [object-を] is-causing seems-[ようですが].
炎症を起こす ('to cause inflammation') is the standard collocation for something becoming inflamed — literally 'to raise an inflammation.' ~ている on 起こす gives the ongoing/resulting state ('is currently inflamed'). ~ようです is the evidential 'looks like / seems' based on visible evidence, and the trailing が softens the utterance the way a doctor might dangle a sentence to introduce a finding — 'it looks inflamed…' as a prelude to further discussion.