Do I need to caulk where the vinyl siding meets the edge of the windows

If you can remove one panel carefully you might find the manufacturer stamp on the back. It will narrow down the search down a little bit. Otherwise just a small sample would be nice to have when visit the stores. I've seen websites on the web that identify manufactures based on the sample that you send. Both Lowe's and Home Depot sell some vynil siding. Not a huge selection.

Honestly, it doesn't have to be exactly the same. The previous owner used a similar siding on the addition and i didn't notice until i had to replace a panel.

Backer rod and sealant is appropriate for joints between dissimilar materials such as that pictured in the question. Preparing the brick surface, correctly sizing the backer rod, and properly installing the sealant may all play a role in long term performance of the system.

Select the sealant for your application based on manufacturer's literature. The label on the tube often contains clear guidance.

Filling voids behind the joint with fiberglass insulation or with spray foam insulation prior to sealing may also improve thermal performance and reduce air infiltration.