If you're talking about the 1990 ABC series "Elvis" starring Michael St. Gerard (which I think had a working title of "Good Rockin' Tonight"), then the "Elvis" singing vocals were all by Ronnie McDowell. "The Mess Around" was featured in the last episode aired, "Let It Burn." Since the series was not on very long, a soundtrack was never released. It sometimes airs with a bunch of the episodes edited together as "Elvis: The Early Years," although I've not run across it in years.
Ronnie McDowell's page includes a CD with "Mess Around" - although I do not know from the description whether or not this is the Ray Charles song as featured in "Elvis" or some other song that happens to have the same title. I would think the odds are that it is the same song, though. http://www.ronniemcdowell.com/order.htm
Hope this helps.