wpdb select doesn't work for searches containing single quotes

I’m having a problem with a $wpdb query selecting results that contain single quotes.

When a user visits a post, a $wpdb query searches the database for all other posts with the same title as the current one and then displays a link to them.

This works fine for all post titles except those with a single quote in them. Other special characters work fine.

A post with the title THE WEATHER: SUNNY will feature a list of all other posts with that title. But a post with the title TODAY’S WEATHER IS NICE will not find any other posts with that title even though several exist, just because it contains a single quote.

I’ve searched for a solution but haven’t found one. Can anyone suggest a way around this?

Here’s the code I’m using:

global $wpdb;
$itemName = get_the_title( $ID );
$results =$wpdb->get_results("SELECT ID FROM $wpdb->posts where  $wpdb->posts.post_title LIKE '$itemName' AND $wpdb->posts.post_status = 'publish' ORDER BY post_title ASC", OBJECT);

foreach ($results as $result){
$newTitle =$wpdb->get_results("SELECT post_title FROM $wpdb->posts where  $wpdb->posts.ID = $result->ID", OBJECT);
printf ($newTitle->post_title);
}

Someone on another forum suggested using wpdb->prepare but, at least with the way I’ve currently implemented it, it still returns the same results. I’d appreciate any suggestions.