I've had ulnar side wrist pain for a couple of years now. The pain was worse when I was holding something with my palm up and it created leverage against my hand, pushing or pulling it down. Like holding a diner plate with my fingers.
The injury happened when I tried to hit a very hard hit shot and the racket twisted in my hand. It would start feeling better then be aggravated again. This pattern went on a while, so I went to the Dr. and got the usual take Aleve, and rest advice. It didn't help, but it's hard for me to completely rest it because of my job which requires a lot of lifting, grabbing, pushing/pulling etc. Went back and finally got an MRI, which showed that I have a partially torn(or healed) ligament in the TFCC. The treatment for now is physical therapy. It's feeling better, and if it does flare up it seems to recover quicker, so hopefully it is continuing to heal. Anyway, you might try looking up exercises for TFCC injuries and see if they help, if you can't get to a Dr.
I also wore wrist supports, but the Dr. never said to wear one or not to. I'd wear a brace at night because I tend to clench my fists and tuck them into my chest. I'd sometimes wake up with achy wrists even before my injury. I also got a support called the wrist widget, that I had mixed results with. It seemed to help at work, but if I played tennis while wearing it, I'd end up getting pain down the outside of my forearm. Now, the only thing I wear is the wrist widget thing if I do weight bearing exercises. I almost feel like I don't need that anymore though.
Anyway, hope your wrist feels better.