Kelly, yes, I would create a new portfolio and use as many programs as you need within the portfolio. Perhaps you use a program for each business area. The good news is that you can move projects around later if you decide on a different organization.
It might help to visualize a filing cabinet to remember the difference between a portfolio and program. The cabinet has all kinds of projects within them. Those projects can be grouped in two ways: a drawer and a file folder. The drawer is the portfolio (because it's the larger way of grouping projects) and the hanging file folder is a program (smaller). The file folder can't work without the drawer because of the specific hanging function; otherwise it just flops around on a desk, right?