The right back side of my neck and head hurts. when i pick anything up it feels like a painful string being pulled. i received a flu shot about 3 hour?

Timing: Which came first? Flu shot or neck pain? You describe very nicely neck muscle spasm which occurs in many different circumstances. Unless your flu shot was injected in your neck, a connection is unlikely. Neck sprain is by far the commonest source of those symptoms, but certainly not the only possibility. Flu symptoms are usually more diffuse, rather than on one side of the neck.