One of the meanings for 'pack up' is to put things in a suitcase, bag or other container so that you may take them with you when you're leaving.
Therefore, when I'm going for a holiday, I'd prefer to say;
"PACK UP MY BELONGINGS"
instead of
"PACK MY BELONGINGS"
or
"PACK MY BAGS".
This is because 'pack your/my/his/her/etc. bags' could mean to leave a place or a job and not return (permanently).
*So, are you packing up or packing your bags? ;)
