If you feel that connection, it's probably there. Symptoms of Addison's include headache and muscle weakness. Muscle weakness can mean that your neck isn't properly supported. Your neck and spine depend on good muscle tone to stay in alignment, and if those muscles are weak, your spine can become out of alignment or discs can bulge, etc., all of which can cause pain. So theoretically it makes sense those things could be related.
I don't know what medication you are on, but if it is some sort of corticosteroid such as prednisone, one of the first symptoms of withdrawal is body aches and pains. Withdrawal can begin with one missed dose.
I'm not sure if this helps you or not. I suggest if the neck pain continues you have your neck checked out, because another thing about steroids is they mask pain. So if something is wrong with your neck and you are taking steroids, the steroids might decrease the pain so you don't realize you have a problem. If the pain continues it is definitely worth a visit to your health care provider.
Here are a couple of resources on Addison's: https://www.empowher.com/addison039s-disease/content/what-addisons-disease?page=0,0; http://endocrine.niddk.nih.gov/pubs/addison/addison.htm.
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