I received a tetanus shot on tuesday. Last night I couldn't sleep because my entire arm and hand were throbbing with pain? What's going on?

Probably nothing . Most likely is a local reaction to the inoculation.
However, if things persist longer than 48-72 hours then seek medical attention .
Shot reaction. This is not an uncommon reaction to a vaccine. Checking the blood for immunity to a specific vaccine is a good idea before getting another one. Once a reaction occurs, the next time could cause a worse reaction.