As you've already highlighted, the best way to do this is via an API. It's actually quite easy to use the Tiny URL API if you have CURL installed:
function get_tiny_url($url) {
$ch = curl_init();
$timeout = 5;
curl_setopt($ch,CURLOPT_URL,'http://tinyurl.com/api-create.php?url='.$url);
curl_setopt($ch,CURLOPT_RETURNTRANSFER,1);
curl_setopt($ch,CURLOPT_CONNECTTIMEOUT,$timeout);
$data = curl_exec($ch);
curl_close($ch);
return $data;
}
//test it out!
$your_url = 'http://mywebsite.com/picture.php?to=' . $rname . '&from=' . $sname . '&message=' . $message . '&amount=' . $amount;
$short_url = get_tiny_url($your_url);
//returns your tiny url
echo $short_url;