I'm just getting used to a road bike, and find that I've been tensing my arms and shoulders, especially when I go over a difficult or anxiety-provoking stretch of road. That might have something to do with your soreness.
So I try to consciously pay attention to keeping my shoulders relaxed (not hunched up to the ears); I don't lock my elbows, but keep them slightly bent. It's interesting, because I find I only need certain muscles for keeping myself steady, for braking, etc... so I try to just use those, and avoid using the unnecessary ones.
Just something you might try.