Just to add, if it only happens after sleeping, then Jon is likely to be right. We do turn over many times in our sleep so the side you wake up on isn't necessarily the side you slept on all night.
It could be carpal tunnel. Tingling is very common but should be investigated.
Most common causes of tingling...
Around a third of cases are the start of diabetes, due to nerve damage.
Kidney disorders, Liver disease, blood disease, hormone imbalance, growths pressing on nerves, vitamin E, b1, b6, b12 and niacin deficiencies, alcoholism, carpal tunnel, ulnar/peroneal/radial nerve palsy, arm position putting pressure on nerves in neck/spine.
If it is in the neck, great, but I think it's best to check for other more serious issues first because the sooner they are addressed the better.
I get that all the time also. I have a very bad neck. Always sleep in the wrong way. Too many pillows. It's like Jon said, a nerve is being pinched. But then my doctor tells me it's carpal tunnel.
In addition I would ask for some blood tests, a low reading of vitamin B12 for example can be the cause.
Your neck is the key to tingling in the hands. If you sleep in an awkward position you can easily pinch a nerve in your neck or shoulders and cause the tingling sensation. Have you reported this to your doctor? If not, you should run it by them.
Jon