1.πονάω = I suffer, I feel pain (as in the first verse)
"πονάς, γιατί σκέφτεσ’ εμένα" = "You suffer, because you are thinking of me"
2.πονάω κάποιον = I hurt somebody
example: Τα λόγια σου με πονάνε" = "Your words hurt me"
3. πονάω κάποιον = feel for somebody, feel compassion (as in the second verse)
δε με πονάς = you don't feel for me
The context will help you to decide between the 2nd and the 3rd meaning.