First of all, keep in mind that I am unable to diagnose you because I am unable to examine you, this forum is for educational purposes.
The symptoms and story that you provide are concerning for some process interupting the flow of nerve signals from the spinal cord to the hand/arm muscles. The process begins at the alpha motor neuron (in the spinal cord) which projects an axon (wire) out of the spinal column through a network of nerves (the brachial plexus) and eventually to the muscles. A disruption at any point in this process can cause weakness and atrophy of the muscles (with abnormal EMGs). Some diseases that affect the alpha motor neuron include ALS and Polio. Radiculopathy (pinched nerve) and root avulsion affect nerves as they exit the spinal column. Trauma, diabetes, neuralgic amyotrophy, compression injuries all can affect the brachial plexus. Compression of peripheral nerves are also quite common including compression of the radial nerve at the spiral groove (of the humerous (upper arm bone)), compression of the ulnar nerve at the elbow (funny bone) and compression of the median nerve at the wrist (carpal tunnel syndrome). Given the history that you have provided, I can not localize your problems any further, but would recommend an MRI of the cervical spine, and a repeat EMG at a major academic center. As far a Depo-Provera shots go, it is likely unrelated. The side effect 'paralysis' is listed in the less than 1% of possible reactions to the medication and has no statistically significant association (there is also no information provided about a possible mechanism). One side effect that is very real is osteoporosis (thinning of the bones). With long term use, you may be at risk for compression fractures of the vertebrae (which can cause a pinched nerve or 'radiculopathy'). But given your age and the fact that you have only used it for three years, this is less likely. I hope this has been helpful.
But I have had cognitive problems, short term memory loss, and attention deficet like problems, 2 brain lesions, doctors don't want to say anything bad about Depo, but once I stopped it, all my problems started.
Hope this helps some
Sounds like a payoff to me.
Search web for depoprovera, you will see what some women are saying.