Translation:My hand hurts.
手 here can mean "arm(s)" too, yeah? Just tried, "My arm hurts" and got marked as incorrect. Checked a dictionary and got these two definitions:
The upper limbs of the human body. The part extending from the left and right shoulders of the upper torso. The part from the shoulder joints to the tip of the fingers.
The part [of that] starting at the wrists. Also used not of this entire section, but vaguely of the fingers, palms etc.
Like I said before, the "hand" meaning seems to be more frequent, but the "arm" meaning is also possible. Also, there is a little ambiguity on what the definition of "手" as "hand" is (it may or not include the wrist) . Here are the two main definitions of "手" according to the Japanese dictionary goo:
㋐人体の左右の肩から出ている長い部分。肩から指先までをいう。俗に動物の前肢をいうこともある。「手を高く上げる」「袖に手を通す」「手の長い猿」 (The long part that comes out of both shoulders in the human body. It refers to (what goes) from the shoulder to the fingertips. It's also how animal forelimbs are commonly called. "I raise my arm high" "I put my arms in the sleeves" "A monkey with long arms" )
㋑手首、手首から指先までや、手のひら・指などを漠然とさす。「手に時計をはめる」「火鉢に手をかざす」「手でつまむ」 (It vaguely indicates (parts) such as (the one) from the wrist to the fingertips, or the palm and its fingers. "I put the watch on my 'hand'(wrist)" "I hold out my hands over the brazier" "I pinch/pick up (something) with my hands" )