This is an interesting question. From your description, a few things could be going on. The tendons of the arm (just like the nerves and blood vessels there) run through relatively narrow spaces, simply because the wrist is a pretty small place. Because of this, the tendons/nerves/blood vessels are at a greater risk of entrapment and of having pressure put on them by surrounding structures (either normal or abnormal).
You could have a tendonitis, an inflammation of one of the tendons in the wrist. This could have been caused by a variety of things, and this can resolve on its own, but it can also require therapy. Generally, motion will make the pain worse. You could also have a small mass in the arm that is putting pressure on the tendons there. This could be an abscess, or even a tumor of some sort (not all tumors are cancer). Just as a tendon can have pressure applied to it, so can a nerve. It is also possible that inflammation or a mass in the wrist is also putting pressure on a nerve resulting in pain.
You don't mention any numbness or tingling, so this makes pressure on a nerve less likely. Similarly, you also don't mention any discoloration of the skin, or other signs of infection. It is possible that you might have a tendonitis.
I would make an appointment with your primary care physician ASAP and go in for a good exam and workup. If it is tendonitis, then it can resolve on its own, but tendonitis of the forearm (besides tennis elbow, which doesn't match your description) is unusual, and so I think you should have it looked at and worked up.
I hope that I have been of some help. Take care
__________________
If I have helped, then please click the ACCEPT button and leave positive feedback - Thank you, and take care
