Yes the while loop is only used to loop through results a row of output at a time.
If you are expecting just one row of results you dont need it. Although for a bit of extra security you could use "LIMIT 1" on the end of the SQL statment to make sure there is only one row output.
Also if you want to use associative arrays, use
mysql_fetch_array($result, MYSQL_ASSOC
Here it is in full:
$sql_db=mysql_query ("SELECT USERNAME FROM UACCNT WHERE USERNAME = '%ME%' LIMIT 1");
$get_username = ($username = mysql_fetch_array($sql_db, MYSQL_ASSOC));
echo $username ['USERNAME'];