What might happen if you were hit hard on the side of the head - - towards the middle

I believe you are talking about the temple of your head? Potentially you can get very serious injurys and complications from being hit their.

You may experience epidural hematoma or other symptoms

You could possibly have a concussion. I would say go to the doctor to see if any other damage were to have happen. If you feel nausea, dizzy, seeing splotches there is a mostly then not that you have a concussion; Concussion is when your brain hits the skull and bruises the brain and it starts to swell.