max_allowed_packet is a server setting and needs to be set on the mysql server.
In any case if you're dealing with very large BLOBs / text fields, you should be using prepared statements and streaming the blob in in chunks. I don't know whether this is possible using PHP (It probably isn't possible with the mysql_ functions, only mysqli or PDO).
http://uk.php.net/manual/en/function.mysqli-stmt-send-long-data.php
In any case 1.6 megs should not be a problem (maybe it will be up to 3x more if you're using a multibyte character set).
Look at the server setting and ensure that it's reasonable- I think the default is 16M so should be fine.
Mark