No, suffering is not always a sign of punishment from God. In the story of Job, his friends incorrectly assumed that Job's suffering was a punishment for some hidden sin. However, God made it clear that this was not the case.
While it's true that God sometimes allows suffering to correct or discipline us, it's also true that He sometimes allows suffering for reasons that we may not understand, as was the case with Job. In all cases, God's purposes are ultimately good, and He works in all things for the good of those who love Him (Romans 8:28).