Don't lock your elbows out. I always scold my wife about that one...when we go riding together, she often locks out her elbows, and also splays her hands out to the side, and essentially uses her arms like immobile "stands" or "props" for her upper body. Of course, doing so transmits every last bump, shock etc. through the joints. It also numbs her hands.
You do have to use your musculature somewhat to support yourself. If not, it can be hard on the arms. If you don't engage your triceps and lats as well, you may find yourself "scrunching" your shoulders up as you lean into your locked out arms over longer distances. This could then produce neck pain, as you're fighting your own shoulders and stance to get your head up and eyes level to view the road.
Just a couple of theories. I don't know if you're actually doing any of these things.
If you've been letting your bones do all the supporting, you may find that supporting yourself with your muscles is a bit tiring at first...trust me, that goes away. And not that you're a wimp, it's just muscle groups that you're not used to using this often, or in this way.
My first bike commute I thought would be a piece of cake. Hell, I went on at least three three mile runs a week, minimum. Oh lord, that first morning kicked my butt.
Just some thougts. Glad you're enjoying the new bike. I was actually just about to PM you to see if you got it yet, and how the riding was going!