Finding a medley without the artist will be difficult. Often on older albums or cassettes the artist would simply call the track "Medley" on the disc notes/song list of the cassette and elaborate on the songs of the medley (if they chose to) on the liner notes. Sites like Discogs or allmusic tend to be good at capturing just the song list and infrequently provide elaboration on things like that.

If it was from a live recording, the chances of finding out exactly who it was is even less likely.

A recording may help if the band was well-known enough to be recognizable by their sound.

Discogs only has 2 albums with all 3 of those songs on them, though it doesn't look like they were played in a true medley fashion on the album: the Gus Ingo album Mr Red referenced, and an album by Charlie Pettis, which doesn't appear to be available online.

A very thorough discography of country music is Praguefrank's Country Music Discographies website, you could try poking around there but the combination of names I used didn't turn up anything that looked right. Bear in mind that many of those songs can be found under alternate names; for example, Beaumont Rag can also be found under the names White River Stomp, Possum Rag, etc.