Medically speaking, you should be drawing with your shoulder. Not only is it easier on your wrist, but once you get the hang of it (cause come on, you're not gonna know how to do something perfectly the first time), it also gives you a lot more control over your lines (you can control where the lines actually go instead of just randomly swiping with your wrist hoping for the best).
Keep practicing with your shoulder, and if you really can't seem to get the hang of it after a few weeks of practice, keep doing what you're doing, HOWEVER make sure you are aware of the health risks that come with drawing solely from your wrist (it's a lot like the difference between lifting with your back and lifting with your knees). Be sure to practice proper wrist exercises to keep your wrists from getting sore or getting carpal tunnel (because then you'll be out of commission for a long time, worst case scenario, forever; and that's a big risk vs. just gritting your teeth and learning healthier methods and practices).
Drawing from your shoulder though, I will admit, is a lot harder to do if you use a small drawing tablet. I still draw from my wrist when I use my drawing tablet, however I draw from my shoulder when I'm using sketchbooks, pads, etc. And there's nothing you can do about that, unfortunately 