First of all: good for you for building up strength in your body first! 🙂 A couple of things come to my mind about your problem ..
The thing is, that the connective tissue takes longer than muscles to adapt to the increased stress you put on it through exercising. So these are often the "weak links". They get stronger through weight-bearing exercises though, so keep doing what you're doing in general 🙂 And shaking the hands or arms out is not a bad thing and doesn't mean you're in trouble.
However, "joint discomfort" is not really normal and you might want to take some rest if your joints still feel funky after exercising. With my wrists I just go by feel. If during a workout I get wrist discomfort I do some mobility exercises and do some exercises that don't stress the wrist (e.g. you can do planks on your forearms instead of in a full push-up position). Usually after a few minutes I can use the wrists normally again. If not I stop putting stress on them for that day.
Good recovery techniques during exercise sessions include massage, foam rolling, mobility exercises, or different creams/gels that help with injuries (they also help if you don't have an injury^^) for the forearms and wrists.
On a side note, for taking stress off the wrists in the push-up position I focus on pressing with my fingers into the ground instead of resting all the weight on the wrists.
If you work out in the morning your joints aren't as lubricated as they are later in the day, so you need more warm up than normal. For the wrists I like to do some specific warm-up exercises like these here:
http://www.globalbodyweighttraining.com/wrist-mobility-exercises/
Also, if you're preparing for pole dance, you need a lot of grip strength anyway, which will help with strengthening wrists and elbows as well. So it would be a good idea to work on grip strength as well 🙂