Only show own comments in admin panel

I believe the below should do the trick, just add to your functions.php file.

/**
 * Prevent non-administrator users from viewing others comments.
 */
add_filter( 'comments_list_table_query_args', function( $args ) {
    global $pagenow;

    if ( $pagenow == 'edit-comments.php' ) {
        $user = wp_get_current_user();
        $value = !empty( $args[ 'author__in' ] ) ? $args[ 'author__in' ] : [];

        if ( is_array( $value ) && !in_array( $user->ID, $value ) && !in_array( 'administrator', (array)$user->roles ) ) {
            $value[] = $user->ID;
        }

        $args[ 'author__in' ] = $value;
    }

    return $args;

}, PHP_INT_MAX );

I was able to put this together by viewing the code of wp-admin/edit-comments.php. Within the file I found a call to the class WP_Comments_List_Table (found in wp-admin/includes/class-wp-comments-list-table.php) which extends the WP_List_Table class.

From experience I knew the WP_List_Table requires a method prepare_items() which usually handles the query. In here I found the filter comments_list_table_query_args which allows us to modify the query arguments before the comments query is made.