The origin of distortion (music)

"what was the first song/band to actually use distortion?"

the first guitarist to "invent" distortion was actually Ike Turner from around late 50's or early 60's. The story goes that Ike and his band were travelling to a gig with their equipment tied to the roof over their car. Yadda, yadda, yadda......they hit a bump and one of their amps fell on the ground. When it fell it tore a hold in the speaker. Totally accidental, but distortion none the less.

Ike Turner

Accidental Discoveries

Despite this fertile ground, distortion was still not actively sought out and implemented. Most of the use of early use was discovered by accident by musicians who liked the sound and decided to continue using it.
One of the earliest uses of distortion was on the song “Rocket 88”, performed by The Kings of Rhythm and written by Ike Turner. Although written as a rhythm and blues song, it became one of the earliest rock and roll songs, if not the first, and was later a minor hit for a more familiar band, Bill Haley and the Comets. In any case, the distorted tone came about when rhythm guitarist Willie Kizart arrived at the studio with a damaged amplifier. Producer Sam Phillips later claimed that the amp had fallen off the top of Kizart’s car, while Turner claimed that the amp had been left in the trunk and rain leaked in, causing the damage. In either case the band and Phillips loved the sound, and created what is regarded (though often disputed) as the first recording of distortion.
Around 1956, guitarist Johnny Burnette of the Johnny Burnette Trio had one of the tubes from his tube amp fall out during the show while covering Tiny Bradshaw’s “Train Kept A-Rollin’” (a song that later became a hit for Aerosmith). The audience loved it, and a local critic gave the sound a rave review. This led Burnette to keep the sound once he recorded the song in the studio.
Even as musicians like Willie Johnson and Chuck Berry (whose sound came about from the aforementioned “clipping” method by playing smaller amps to their maximum output) were using the earliest known forms of overdrive, it was not readily accepted, nor was there any device or foot pedal to reproduce the sound. The sound was there; it just hadn’t gained enough attention yet to appeal to the masses.
Once again, distortion needed something big to happen to take the next step forward. This next big step occurred thanks in part to a screwdriver, a Broadway musical, and a good chunk of controversy.