Add a filter to your media so that you can add the oEmbed functionality.

functions.php

<?php
// get media; could be a url to a tweet, or youtube video, or something else;
$media;

$media = apply_filters( "my_media_filter", $media );

// add filter for oEmbed
$media = apply_filters( "my_media_filter", $media );
			
// print embedded media
echo $media;