One of the more common injuries that paddlers get is tendinitis or carpal tunnel in the wrists. One of the more common reasons why is that new paddlers tend to grip their paddle to tight causing unnecessary stress in the wrists and forearms. This is something that instructors need to make students aware of.
There are a couple of different methods to help mitigate this repetitive injury. You can go out and get an ergonomic bent shaft paddle which helps keep your wrists in better alignment or you can focus on gripping the paddle shaft as light as possible and spend some time before paddling stretching and warming up before jumping on the water.
If you do find yourself with tense, sore or inflamed wrists as I often do, you can spend some time going through stretches specifically for your wrists. The video below is a great demonstration of several that are very good in helping to stretch out the tendons again and hopefully bring you some relief.