How do I get old text messages back that are less than 120 days old?

Generally, you don't.

If you have a device backup that includes the message(s), and you do not use messages in iCloud, you can factory reset and erase your device and set it up using your backup. You'll lose anything since the backup was made, but you may recover your message(s). If you only backup to iCloud, those messages are long gone. If you backup to your computer and kept older backups somewhere, you might be able to use that to restore.