I would do it NogDog's way, but if for whatever reason you need to do it your way, you could create an array with the abbreviation/name values and use that when updating/inserting. So basically your form would submit only the abbreviations, and you would get the state name for that abbreviation from an array.
for example:
//state abbr / state name array
$states = array('AL' => 'Alabama', 'AK' => 'ALASKA', ...etc);
//get state abbr from form
$state_abbr = $_GET['state_abbr'];
//get state name for $state_abbr
$state_name = $states[$state_abbr];
$sql = "insert into table (...etc, state_name, state_abbr, ..etc) values (...etc, $state_name, $state_abbr, ..etc)";