I am in the navy and a corpsman told me my pain in my wrist is from over working it. I have had this for over a year in both wrists. What could it be?

Many possibilities. The location of your pain will help narrow down your diagnosis. Common causes of wrist pain include but not limited to tendinitis, strains/sprains, nerve compression and even fractures. Oversue injuries generally cause inflammation of tendons however, other possibilities remain. Therefore proper examination and evaluation by an orthopedist can help diagnose and treat the problem.
Many things. Best to have this looked at if it's really significantly impacting your abilities or significantly painful. Don't underestimate the power of an x-ray. Get it checked and make sure things are ok.
What's your job? Depending on your job, different kinds of overuse injury are possible. Sounds most likely to be tendonitis, though other problems such as carpal tunnel syndrome should be ruled out. A wrist support and nsaids may help. If pain is severe, you should see a doctor who can evaluate and diagnose the exact problem. Rest or temporary transfer to a different position may be needed.