They will callus over soon enough, then you wont have this problem nearly as much.
By the way, the rowing machine is a fantastic all-round exercise. It's important that you are using the correct technique, otherwise you'll be getting less power in each stroke, less fluidity, and you could hurt your back. In general, most of the work should be done by your legs, and then the back, arms and shoulders as you finish each stroke. Kinda hard to explain, try to find a video online for proper technique.
I'd also suggest mixing up your rowing machine regime on each gym visit to keep things interesting. Some long, low intensity workouts with no break. Some short, higher intensity workouts with many breaks. And some in the middle.
Finally, track your times, even better if you use a heart rate monitor! It's a big buzz to see your times get better while your heart rate is at the same range level.