need text messages that didnt back up

If you had turned on Messages in iCloud your content is automatically stored in iCloud and is never backed up and is available on all devices that use the same Apple ID

If they are not in your backup you cannot get them back. If you have other Apple devices and you are using continuity you can look and see if they still appear there (you won't be able to restore them to your iPhone). If you have turned on iCloud Messages they are probably gone.

I understand that you have no backups created of your iPhone ( Computer or iCloud). If this is the case then there is nothing that you have to recover those text messages from. Did you use iCloud for Messages by any chance? If YES, then you can do the same on your new iPhone and those messages should be synced with the new iPhone.

If you did not create backups and you did not use iCloud for Messages, then the only way to recover those messages is by transferring the data from your old iPhone to your new iPhone. This, of course, will only work if you get the old broken iPhone repaired.

Axel F.