I Have Had This Weird Feeling In My Neck, It's Like A Tingling Sensation, And It Goes Down To My Upper Shoulder. What Does That Mean? Is That An Indication Of A Stroke?

Usually this would be termed a crick, a painful tingling which lasts no more than three days. This could have been caused by muscle tension from being asleep or on an aeroplane, causing a horrible spasm which is only treated by rest and liquids, possibly an ice pack to stimulate the muscular movements.

A stroke often occurs when the left-side of the body, in particular the arm, becomes limp and lifeless, though naturally a neck pain would indicate it too. If you are sure that you did not develop the pain from your neck being in an enforced position, and that it is very sudden and is a feeling that goes away then returns, then do consult a physician.

Sometimes people experience a ‘pre-stroke’, a short-term lack of blood supply to the brain, also called a transient ischemic attack. The loss of blood supply lasts from seconds to just a few minutes and does not result in permanent damage. This condition is often a precursor to a full-scale stroke, so any symptoms associated with it should be investigated immediately.

Warning signs of stroke can include ANY of the following sudden happenings: Difficulty in speech or speech comprehension; onset of confusion or loss of consciousness; numbness or dizziness; headache; trouble walking; neck pain; and vision pain. Some regular everyday activities, such as stargazing, rapidly turning the head while driving, and even having a shampoo in a hair salon may cause an aneurysm,a widening of an artery resulting from the weakening of the artery walls, of the neck arteries, resulting in stroke.

If you are visiting your doctor or chiropractor with upper-neck pain or headaches, be very specific about your symptoms, so that they can provide the safest and most effective treatment, even if it involves referral to another health care provider.

There are various head and neck positions and forms of joint movement. Joint mobilization, therapeutic exercise, soft-tissue techniques, and other therapies can be recommended. If the issue of stroke concerns you, do not hesitate to discuss it with your doctor or chiropractor. Neck manipulation can also be advised.

Sounds like a pinched nerve to me, and this could be brought on by stress causing your neck muscles to tense up.   I've had pinched nerves in my neck for 20+ years, and that was how they started!  I agree with 3rd-MAW's advice!  Go see your doctor!
-WB

Probably spending to much time in front of comp. Try lowering monitor or raising your seat. Your dr. Will probably do an ultrasound to check circulation. But it really doesn't sound like a stroke.

Hmmm. So you definitely don't think its a stroke? Cause I was really worried about that. I keep doing neck exercises and it seems to be helping, but only for a minute or two. Then it comes back. I'm not at the computer too often. But I guess I could try that. What other advice do you have? Thank you by the way.

Could be early warning sign of stroke or a pinched nerve due to a bulging disc or arthritis in the neck, which could cause bone spurs to grow and push on the nerves in your spinal cord.
Are the muscles in your neck tensing up? That could also put pressure on the nerves in your neck which run down your arms. 
Sounds like you need to see a doctor to have it checked just to be safe. The sooner, the better.