how do i get my old messages off my iphone

If these are messages you received, then is it possible that you have your messages set to delete after a certain time? If you go to Settings>Messages>look under Message History what is the setting there? If not set to Forever, it is possible the messages were automatically deleted. Otherwise you would have needed to restore your backup. But if the messages were deleted sometime in the past, they will no longer be in backup.

Were you using iCloud Messages at that time? Or are you saying messages downloaded to iCloud meaning that you created a backup in iCloud? There is a big difference. When did you turn on iCloud Messages?

If you are using iCloud Messages, you log into iCloud on the new phone and turn on the switch for Messages.