I don't think you've much chance. Text messages are stored in a database (not as separate files) in an area of the phone's storage that's not visible to the user without root and not visible to a PC at all (so forget file recovery software on a PC, which in any case won't work over USB because the phone is connected as an MTP device rather than USB Mass Storage).
If you were rooted you could copy the database to a PC then see whether the deleted text is still in there (just flagged as deleted) or not. The database will be /data/data/com.android.providers.telephony/databases/mmssmsdb, so if you have root access and a file explorer app you could copy (not move!) it to somewhere a PC can see it. But I'll be a bit surprised if the data would still be there.