How can i check if a variable is saved or not in the db?

mysql_num_rows

if(mysql_num_rows($sql) == 0) {
    //Show error 
}

You can use the following query:

"SELECT COUNT(*) FROM `videos` WHERE `id` = ".mysql_real_escape_string($local_id)

This query will return one number: how many records have matched your query. If this is zero, you surely know that there are no records with this ID.

This is more optimal than other solutions posted in case you only want to check for the existence of the ID, and don't need the data (if you use SELECT * ..., all the data will be unnecessarily sent from MySQL to you). Otherwise mysql_num_rows() is the best choice, as @Ryan Doherty correctly posted.

Be sure to ALWAYS escape data that came from the outside (this time GET) before you put it into a query (mysql_real_escape_string() for MySQL).

If you fail to do so, you are a possible victim for SQL Injection.

$sql = dbquery("select count(*) from videos where id = ".$local_id." LIMIT 0, 1");
$row = mysql_fetch_row($sql);
if($row[0] == 0)
    echo 'error';

You could have a $count variable and increment it in the while loop. After the loop, check the count, if it is 0, then echo an error message.