Wrist pain when I move it up and down but not side to side. Even pulling my hand does not hurt. It seems to get better but always comes back. Thank yo?

Many possibilities. At the top of the list would be some form of wrist tendonitis but other possibilities would include latent injury such as unrecognized scaphoid fracture, ligament sprains, occult masses such as ganglia, avn of the lunate (kienbock's), and tfcc injury (though surely not a classic description). You should have a good exam with plain x-rays and possibly an mri. Best of luck.
Wrist ARTHRITIS. My bet is that this is most likely arthritis. Tendinitis like "intersection syndrome" can cause pain with up/down motion, but usually has some swelling just above (not at) the wrist and some "crunching" feeling there. There are other causes, of course, so see a hand surgeon for an exam and at least an x-ray. You'll be happy you did.