If I move my head a certain way, I can feel a painful tightness from right neck thru right head. Could it be pulled muscle or nerve?

Neck muscle strain. You likely strained/injured your posterior long cervical neck muscles. Rest, NSAIDs, and very mild stretching as tolerated will likely hasten your expected full recovery. If symptoms persist despite doing these things for more than several weeks, seek medical attention for a thorough evaluation.