In your example it could be referring to either physical or emotional distress.
The words 'hurt' and 'pain' both have noun, verb and adjective forms.
However, in regards to modern colloquial English usage, 'hurt' is more often used to describe mental or emotional distress than 'pain'.
Your harsh words 'hurt' my feelings.
The girl felt 'hurt' by her boyfriend's breaking up with her.
His pride was 'hurt' by his boss's criticisms.