After wrestling the right side of my neck and my upper chest hurts when I breath in deeply. What could this be from? . .. Pinched nerve maybe. ..?

Probably not nerve. Sounds more like some strained muscles in your neck and chest. A pinched nerve in the neck would send pain down your arm.
More Likely A Strain. More than likely, it is muscle strain rather than a pinched nerve, based on the location of the pain. Treat it like any other strain (rest, ice, non-prescription pain medication) and if it is not better within a couple of days, see your doctor.