When I bite down on my right side, I get a sharp pain in the right back side of my head. What could this be?

TMJ pain. The pain probably originates in the temporomandibular joint. A issue with a tooth could also be the cause. Ask your dentist to evaluate the problem.
Jaw or neck issue. Sometimes it could be your jaw joint or a tooth issue referred to the dental nerve. Sometimes it's a neck nerve issue.