sore and painful

hurt　動詞　痛む

sore 　(形容詞）　痛い　　痛みの部分に使う

私の背中が痛い-----> My back is sore./ My back hurts.
私の手首が痛い-----> My wrist is sore.
彼女の脚が痛い(彼女は脚が痛い）----->Her legs are sore.
わたしはまだ少し痛い------> I'm still a little sore. / I still hurts a little.
私の喉は痛い-----> My throat is sore.


Painful （形容詞）痛みをもたらす　　痛みの原因の時に使う
日焼けが痛い------> A sunburn is painful.
歯痛は痛い-----> A toothache is painful.
私の手術は痛かった-----> My operation was painful. / My operation hurt.
腕をあげるのは痛い-----> Raising my arm is painful.
飲み込むのは痛い-----> Swallowing is painful. / Swallowing hurts.
私の猫が死んだ記憶はまだとても辛い-----> The memory of my cat's death is still very painful.
---------> The memory of my cat's death still hurts a lot.

*日本語では　頭痛が痛いとは言わないです。「歯痛は痛い」は日本語的にはおかしい感じがしますが、A toothache is painful.は正しい言い方です