The Carthaginians were eventually completely destroyed so I guess we can forgive their silence. But as these wars involved many lands and affected many cities, do we have any historical accounts of these wars from anyone other than the Romans themselves?
To answer your question literally - yes. Polybius, Plutarch and Appian were Greeks by birth, with Polybius providing the fullest account of the wars.
To answer your question in the spirit in which it was intended - no. While there is some uncertainty about how much historiographic tradition there was for the Carthaginians anyway (see the excellent discussion here by /u/publiusclodius for more details), it is worth considering that the Punic Wars may have affected many cities and geographically distinct places, but all of them were either under Roman or Carthaginian control; there is no "knock on" effect for the other major players in the Mediterranean at the time, particularly with the Seleucid wars going on in the Aegean.