What causes slight bulg in back neck (base of skull) extreme pain that shoots through my head into left eye and gives me extreme migraine soon after?

Occipital neuralgia . This maybe related to irritation to nerve behind the head called the occipital nerve. Recommend visiting pcp.
Cluster Headache. Read this first===>http://en.Wikipedia.Org/wiki/cluster_headache. Many sufferers of these so-called "cluster headaches" describe a neck bulge and post ictal soreness like you and a very intense, insufferable migraine-like pain, unilaterally. We don't know what causes cluster headaches, but smoking is often a trigger. The article describes possible treatments.
Seek evaluation. Any atypical growth, bulge or swelling, especially one that causes pain and other symptoms is well worth having evaluated. Start with your primary care doctor but reach out while you are motivated!
Tension and occipita. Neuropathy (impingement of the occipital nerve coming out of a foramen at the back of the skull next to where you feel the bulge) are common causes of the type of headache you're explaining. Icing around the area, neck massage and anti-inflammatories are effective treatments.

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