My elbow hurts. Maybe I should go to the hospital.

Literal

Elbow [subject-が] hurts [emphasis-んだよ]. Hospital [to-に] going [wonder-かな].

痛むんだよ uses the explanatory んだ + よ to assert a complaint. 行こうかな uses the volitional + かな for self-directed deliberation — 'I wonder if I should go.' Natural casual speech about a health concern.