I have a wound on my arm and it's not getting better. It's still throbs all the time.
この場合、次のような言い方ができますよ。
ーI have a wound on my arm and it's not getting better. It's still throbs all the time.
「腕の傷が良くならなくて、ずっと疼いている」
傷がうずくことは to throb を使って表現できますよ。
ご参考まで!