。
My eyes sting.
Literal
Eye [subject-が] sting-sting does.
ヒリヒリ is a 擬態語 (state mimetic) specifically for a stinging, burning, prickly sensation — think sunburn, eye irritation from smoke, or spicy food on the lips. Attaches to する to form an event-verb: 'to do [the stinging state]' = 'to sting.' Mimetics like these deliver the kind of fine sensory precision English handles with adjectives or longer phrases.