Apple saves your text messages in its iPhone backups—whether they're saved locally on your PC or they're part of an iCloud backup—which you should have. That's good! Unfortunately, the file containing your messages doesn't appear separately within the backup. However, you can access them through the filesystem. If you back up locally on an Apple computer, you can find the file under Library > Application Support > MobileSync > Backup. You should find multiple folders in there, each with a different backup image of your phone.