一生懸命指でまぶたを広げて目薬を差しました。

。

I spread my eyelids as wide as I could with my fingers and put in the eye drops.

Literal

Wholeheartedly fingers [with-で] eyelids [object-を] spread-open eye-drops [object-を] administered.

一生懸命 ('with all one's might') applied to the mundane act of putting in eye drops creates a humorous image of struggle. 目薬を差す ('to administer eye drops') uses 差す, the specific verb for applying drops. まぶたを広げる ('to spread one's eyelids') vividly describes the universal struggle of keeping eyes open for drops.