I'm not too familiar with InfoPath 2003, my specialty is 2007 and 2010.
However, in 2007 and 2010 you have the idea of "Repeating" elements - basically items that can have multiple entries. Can you use that? If it works like 2007, then all you have to do is click the properties of the field in which you wish to store data. Click the checkbox next to Repeating. Then in your form, place a Repeating Table (if you click the dropdown next to the field it should give you that choice).
Then what the user sees is something like this:
______________________________________
|New Field |
|-------------------------------------|
|[Text Box Here] |
---------------------------------------
[Image] Click here to insert item
Every time they want another item added to the list, they just have to click "Click here to insert item"
[EDIT] I can't get the formatting right, but you get the idea - it's in a table.