Learn HOW to fall... SERIOUSLY! I wish someone told me how to do it right the first day... my wrists would be much happier. Needless to say, just like another poster mentioned, I highly recommend wrist guards. If you don't have them, get thick gloves and do one of two things... 1.) Use your elbow instead of your wrists to cushion the fall or 2.) Punch the ground like you're doing close-fisted push-ups. Whichever you use will depend on the angle of your fall. It's important to do this not just to protect your wrists, but also you're noggin. My wife started the same day I did and got a minor concussion because she didn't fall properly after a heelside slip.
From your post, I suspect you're a full grown adult. Full grown adults don't fall nearly as nicely as small children. Your center of gravity is higher, which means your falls are harder. Unless you're consistently falling in soft powder, expect a lot of pain the next day due mostly to the falling and not the snowboarding itself. Once you get better, your lower body will start hurting more than your upper body.
That's a reason why I wouldn't recommend a lesson on the second day. If you put a full day on hardpack/ice like we did on the first day, a lesson on the second day would have probably been torture.