Could That Shoulder Pain Really Stem From the Neck?
Pain felt in the shoulder is often assumed to start in the shoulder. A documented source can say whether looking at the neck first makes sense.
What Cleveland Clinic describes
Cleveland Clinic's neck pain page describes a shooting pain that travels from the neck to the shoulders or arms. That sentence says pain can travel from the neck into the shoulder region, so yes, it is possible.
Why a firm answer needs an exam
Cleveland Clinic does not say how often shoulder pain begins in the neck, and it gives no test for telling the two apart. Be cautious with a quick self-check that promises a firm answer. Sorting out where pain starts takes an examination, so no list of symptoms on a website can settle it for you.
Notes to bring about your neck and shoulder
Note which movements bring the pain on, whether turning or tilting your head changes it, and whether the pain feels the same on both sides. Read the Spine-health page on neck pain causes, the MedlinePlus topic page on neck injuries and disorders, and the Cleveland Clinic guide to common causes and treatments of neck pain to compare how each describes neck pain. Then bring your notes to a clinician in Totowa or nearby and ask directly whether the shoulder pain could come from the neck and how they would tell.

From possible to answered
Possible is not the same as likely, and only an exam moves a possibility to an answer.