I have chronic pain in my arms and I don't know why? What could it be?

Arm pain. It could be several different things. If it is chronic or long standing, it should be worked up. Your doctor will consider nerve trauma, nerve irritation, disc herniation, spinal pathology, nerve entrapment, neuropathy, metabolic disturbances and many other conditions. Best to find out and treat the source!
Spine vs Extremities. There is the possibility this arm pain could be coming from the neck, however the other options include peripheral nerve entrapments, carpal tunnel and ulnar tunnel syndromes. In order to narrow down the possibilities we would need more info. If concerned, please see your doctor to further evaluate you.
Info incomplete. Many questions need answers like time of onset. Whether it started in one arm. Neck pain present or not. Best option would be to see a neurologist and some other specialist may need to be seen.
Might be aneurysm. This can be an aneurysm in the aorta causing increased pressure in the arms, and pain, or some other circulation problem. It might be a lymphatic issue, but your arms would likely be swollen. It can also be due to muscle pain from reduced blood supply or excessive exercise, or some other reason. If it is present at rest, and doesn't go away with aspirin/analgesics, you should see your doctor.