I have a gone to sleep feelining that turns into a feeling of something pulling down on my shoulder. Starts on the left side of my neck back and chest?

Need to rule out. Heart problem. Some patients have atypical symptoms due to heart disease, especially women. Do not know your gender, age, or your health status. If heart disease is even a remote possibility, get yourself checked out asap.
? mechanical. It's probably mechanical, from the muscles in the neck tractioning on the muscles and tendons that course from them and go towards the arm, shoulder, and around chest. Could also be a pinched nerve. Would need an exam and feel the exact texture of the muscles involved in order to get a better idea of what is causing this per se.