When I squeeze my left hand I get a shooting pain from my hand to my elbow. If I leave my arm in one position too long it gets sore and hard to move.?

Arthritis. It's not clear. Symptoms of arthritis are pain on movement after periods of rest which improve with gentle motion and heat. Often hands that are painful in the morning and get better as things get "warmed up" suggest osteoarthritis.
Arthritis/tendonitis. Both of the above can cause these symtoms and an evaluation by your doctor should be able to diagnose the problem.

Related Questions

The joints in my left hand are stiff and sore, wrist is also somewhat sore, and shooting pain up to my elbow. Pain is aching, though may burn in am.

carpel tunnel. It sounds like a repetitive stress injury such as carpel tunnel syndrome. You must ice the area, take nsaids, and avoid the stressful use of that hand. If all else fails, see a hand doctor.