Ridge Crossing in Saltillo, just north of Tupelo, shoots IDPA.
http://www.ridgecrossingshootingclub.com/index.php
CRSSA in Glen, between Corinth and Iuka shoots USPSA/IPSC
http://www.crssa.com/
They also have some other events.
There are clubs in Sheffield, AL (IDPA, .22 novelty shoots) and Memphis, TN (IDPA, USPSA, NRA) that might be within your "combat radius" for those sports.
http://dwightpilkilton.proboards.com/index.cgi?
http://www.memphis-ssa.com/
www.idpa.com and
www.uspsa.org have club finders you can look at for other locations where those sports are shot.